In the form \(\frac{3\pi}{2}+x\), \(\sin\) changes to \(\cos\) with a negative sign. Hence the answer is \(-\cos x\).
Step 2
Why this answer is correct
The correct answer is A. -\(\cos x\). In the form \(\frac{3\pi}{2}+x\), \(\sin\) changes to \(\cos\) with a negative sign. Hence the answer is \(-\cos x\).
Step 3
Exam Tip
\(\frac{3\pi}{2}+x\) रूप में \(\sin\) बदलकर \(\cos\) होता है और चिन्ह ऋणात्मक होता है। इसलिए उत्तर \(-\cos x\) है।
(\sin\(\frac{\pi}{2}-x\)=\cos x), so (\cosec\(\frac{\pi}{2}-x\)=\frac{1}{\cos x}=\sec x). Use reciprocal and cofunction identities together.
Step 2
Why this answer is correct
The correct answer is A. \(\sec x\). (\sin\(\frac{\pi}{2}-x\)=\cos x), so (\cosec\(\frac{\pi}{2}-x\)=\frac{1}{\cos x}=\sec x). Use reciprocal and cofunction identities together.
Step 3
Exam Tip
(\sin\(\frac{\pi}{2}-x\)=\cos x), इसलिए (\cosec\(\frac{\pi}{2}-x\)=\frac{1}{\cos x}=\sec x)। व्युत्क्रम और पूरक पहचान साथ लगाएँ।
(\cos\(\frac{\pi}{2}-x\)=\sin x), so (\sec\(\frac{\pi}{2}-x\)=\frac{1}{\sin x}=\cosec x). Complementary angles give cofunctions.
Step 2
Why this answer is correct
The correct answer is C. \(\cosec x\). (\cos\(\frac{\pi}{2}-x\)=\sin x), so (\sec\(\frac{\pi}{2}-x\)=\frac{1}{\sin x}=\cosec x). Complementary angles give cofunctions.
Step 3
Exam Tip
(\cos\(\frac{\pi}{2}-x\)=\sin x), इसलिए (\sec\(\frac{\pi}{2}-x\)=\frac{1}{\sin x}=\cosec x)। पूरक कोण में सहफलन बनता है।
At \(\frac{\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{\pi}{2}+x\)=-\cot x).
Step 2
Why this answer is correct
The correct answer is A. \(-\cot x\). At \(\frac{\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{\pi}{2}+x\)=-\cot x).
Step 3
Exam Tip
\(\frac{\pi}{2}+x\) पर \(\tan\) बदलकर \(\cot\) होता है और चिन्ह ऋणात्मक होता है। इसलिए (\tan\(\frac{\pi}{2}+x\)=-\cot x)।
In the form \(\frac{\pi}{2}+x\), \(\cos\) changes to \(\sin\) with a negative sign. Hence it becomes \(-\sin x\).
Step 2
Why this answer is correct
The correct answer is B. \(-\sin x\). In the form \(\frac{\pi}{2}+x\), \(\cos\) changes to \(\sin\) with a negative sign. Hence it becomes \(-\sin x\).
Step 3
Exam Tip
\(\frac{\pi}{2}+x\) वाले रूप में \(\cos\) बदलकर \(\sin\) होता है और चिन्ह ऋणात्मक होता है। इसलिए \(-\sin x\) मिलता है।
In the form \(\frac{\pi}{2}+x\), \(\sin\) changes to \(\cos\) and the sign remains positive. Hence the answer is \(\cos x\).
Step 2
Why this answer is correct
The correct answer is D. \(\cos x\). In the form \(\frac{\pi}{2}+x\), \(\sin\) changes to \(\cos\) and the sign remains positive. Hence the answer is \(\cos x\).
Step 3
Exam Tip
\(\frac{\pi}{2}+x\) वाले रूप में \(\sin\) बदलकर \(\cos\) होता है और चिन्ह धनात्मक रहता है। इसलिए उत्तर \(\cos x\) है।
For a complementary angle with \(\frac{\pi}{2}\), \(\tan x\) changes to \(\cot x\). Remember cofunction identities.
Step 2
Why this answer is correct
The correct answer is B. \(\cot x\). For a complementary angle with \(\frac{\pi}{2}\), \(\tan x\) changes to \(\cot x\). Remember cofunction identities.
Step 3
Exam Tip
\(\frac{\pi}{2}\) के पूरक कोण में \(\tan x\) बदलकर \(\cot x\) हो जाता है। पूरक पहचान याद रखें।
By the complementary angle identity, (\cos\(\frac{\pi}{2}-x\)=\sin x). In such questions, \(\sin x\) and \(\cos x\) interchange.
Step 2
Why this answer is correct
The correct answer is D. \(\sin x\). By the complementary angle identity, (\cos\(\frac{\pi}{2}-x\)=\sin x). In such questions, \(\sin x\) and \(\cos x\) interchange.
Step 3
Exam Tip
पूरक कोण पहचान से (\cos\(\frac{\pi}{2}-x\)=\sin x) होता है। ऐसे प्रश्नों में \(\sin x\) और \(\cos x\) आपस में बदलते हैं।
By the complementary angle identity, (\sin\(\frac{\pi}{2}-x\)=\cos x). With \(\frac{\pi}{2}\), the function changes.
Step 2
Why this answer is correct
The correct answer is C. \(\cos x\). By the complementary angle identity, (\sin\(\frac{\pi}{2}-x\)=\cos x). With \(\frac{\pi}{2}\), the function changes.
Step 3
Exam Tip
पूरक कोण पहचान से (\sin\(\frac{\pi}{2}-x\)=\cos x) होता है। \(\frac{\pi}{2}\) के साथ फलन बदलता है।
(\sin\left\(\frac{3\pi}{2}+\theta\right\)=-\cos \theta). In a \(\frac{3\pi}{2}\) form, \(\sin \theta\) changes to its cofunction.
Step 2
Why this answer is correct
The correct answer is C. -\(\cos \theta\). (\sin\left\(\frac{3\pi}{2}+\theta\right\)=-\cos \theta). In a \(\frac{3\pi}{2}\) form, \(\sin \theta\) changes to its cofunction.
Step 3
Exam Tip
(\sin\left\(\frac{3\pi}{2}+\theta\right\)=-\cos \theta) होता है। \(\frac{3\pi}{2}\) वाले रूप में \(\sin \theta\) सह-फलन में बदलता है।
With \(\frac{3\pi}{2}\), \(\cos \theta\) changes to the cofunction \(\sin \theta\). In the third quadrant, \(\cos \theta\) is negative.
Step 2
Why this answer is correct
The correct answer is A. -\(\sin \theta\). With \(\frac{3\pi}{2}\), \(\cos \theta\) changes to the cofunction \(\sin \theta\). In the third quadrant, \(\cos \theta\) is negative.
Step 3
Exam Tip
\(\frac{3\pi}{2}\) के साथ \(\cos \theta\) सह-फलन \(\sin \theta\) में बदलता है। तीसरे चतुर्थांश में \(\cos \theta\) ऋणात्मक होता है।
With \(\frac{3\pi}{2}\), \(\sin \theta\) changes to a cofunction and the sign is negative in the third quadrant. So the answer is \(-\cos \theta\).
Step 2
Why this answer is correct
The correct answer is C. -\(\cos \theta\). With \(\frac{3\pi}{2}\), \(\sin \theta\) changes to a cofunction and the sign is negative in the third quadrant. So the answer is \(-\cos \theta\).
Step 3
Exam Tip
\(\frac{3\pi}{2}\) के साथ \(\sin \theta\) सह-फलन में बदलता है और तीसरे चतुर्थांश में चिह्न ऋणात्मक होता है। इसलिए उत्तर \(-\cos \theta\) है।
The cofunction of \(\cosec \theta\) is \(\sec \theta\), and the sign remains positive in the second quadrant. Remember cofunction pairs.
Step 2
Why this answer is correct
The correct answer is B. \(\sec \theta\). The cofunction of \(\cosec \theta\) is \(\sec \theta\), and the sign remains positive in the second quadrant. Remember cofunction pairs.
Step 3
Exam Tip
\(\cosec \theta\) का सह-फलन \(\sec \theta\) है और दूसरे चतुर्थांश में चिह्न धनात्मक रहता है। सह-फलन जोड़ों को याद रखें।
The cofunction of \(\sec \theta\) is \(\cosec \theta\), and \(\sec \theta\) is negative in the second quadrant. Hence the value is \(-\cosec \theta\).
Step 2
Why this answer is correct
The correct answer is A. -\(\cosec \theta\). The cofunction of \(\sec \theta\) is \(\cosec \theta\), and \(\sec \theta\) is negative in the second quadrant. Hence the value is \(-\cosec \theta\).
Step 3
Exam Tip
\(\sec \theta\) का सह-फलन \(\cosec \theta\) है और दूसरे चतुर्थांश में \(\sec \theta\) ऋणात्मक होता है। इसलिए मान \(-\cosec \theta\) है।
The cofunction of \(\cot \theta\) is \(\tan \theta\), and the sign is negative in the second quadrant. In such questions, first identify the cofunction.
Step 2
Why this answer is correct
The correct answer is D. -\(\tan \theta\). The cofunction of \(\cot \theta\) is \(\tan \theta\), and the sign is negative in the second quadrant. In such questions, first identify the cofunction.
Step 3
Exam Tip
\(\cot \theta\) का सह-फलन \(\tan \theta\) है और दूसरे चतुर्थांश में चिह्न ऋणात्मक होता है। ऐसे प्रश्नों में पहले सह-फलन पहचानें।
The cofunction of \(\tan \theta\) is \(\cot \theta\), and the sign is negative in the second quadrant. Therefore the answer is \(-\cot \theta\).
Step 2
Why this answer is correct
The correct answer is C. -\(\cot \theta\). The cofunction of \(\tan \theta\) is \(\cot \theta\), and the sign is negative in the second quadrant. Therefore the answer is \(-\cot \theta\).
Step 3
Exam Tip
\(\tan \theta\) का सह-फलन \(\cot \theta\) है और दूसरे चतुर्थांश में चिह्न ऋणात्मक होता है। इसलिए उत्तर \(-\cot \theta\) है।
(\cos\left\(\frac{\pi}{2}+\theta\right\)=-\sin \theta). At \(\frac{\pi}{2}\), the function changes and the sign is decided by the quadrant.
Step 2
Why this answer is correct
The correct answer is B. -\(\sin \theta\). (\cos\left\(\frac{\pi}{2}+\theta\right\)=-\sin \theta). At \(\frac{\pi}{2}\), the function changes and the sign is decided by the quadrant.
Step 3
Exam Tip
(\cos\left\(\frac{\pi}{2}+\theta\right\)=-\sin \theta) होता है। \(\frac{\pi}{2}\) पर फलन बदलता है और चिह्न चतुर्थांश से तय होता है।
With \(\frac{\pi}{2}\), \(\sin \theta\) changes to its cofunction \(\cos \theta\). The sign remains positive in the second quadrant.
Step 2
Why this answer is correct
The correct answer is A. \(\cos \theta\). With \(\frac{\pi}{2}\), \(\sin \theta\) changes to its cofunction \(\cos \theta\). The sign remains positive in the second quadrant.
Step 3
Exam Tip
\(\frac{\pi}{2}\) के साथ \(\sin \theta\) सह-फलन \(\cos \theta\) में बदलता है। दूसरे चतुर्थांश में चिह्न धनात्मक रहता है।
(\sec\left\(\frac{\pi}{2}-\theta\right\)=\cosec \theta). \(\sec \theta\) and \(\cosec \theta\) are cofunctions.
Step 2
Why this answer is correct
The correct answer is D. \(\cosec \theta\). (\sec\left\(\frac{\pi}{2}-\theta\right\)=\cosec \theta). \(\sec \theta\) and \(\cosec \theta\) are cofunctions.
Step 3
Exam Tip
(\sec\left\(\frac{\pi}{2}-\theta\right\)=\cosec \theta) होता है। \(\sec \theta\) और \(\cosec \theta\) सह-फलन हैं।
(\cos\left\(\frac{\pi}{2}-\theta\right\)=\sin \theta). In cofunction relations, \(\sin \theta\) and \(\cos \theta\) interchange.
Step 2
Why this answer is correct
The correct answer is B. \(\sin \theta\). (\cos\left\(\frac{\pi}{2}-\theta\right\)=\sin \theta). In cofunction relations, \(\sin \theta\) and \(\cos \theta\) interchange.
Step 3
Exam Tip
(\cos\left\(\frac{\pi}{2}-\theta\right\)=\sin \theta) होता है। सह-फलन संबंध में \(\sin \theta\) और \(\cos \theta\) आपस में बदलते हैं।
(\sin\left\(\frac{\pi}{2}-\theta\right\)=\cos \theta) is a cofunction relation. In transformations with \(\frac{\pi}{2}\), the function changes.
Step 2
Why this answer is correct
The correct answer is A. \(\cos \theta\). (\sin\left\(\frac{\pi}{2}-\theta\right\)=\cos \theta) is a cofunction relation. In transformations with \(\frac{\pi}{2}\), the function changes.
Step 3
Exam Tip
(\sin\left\(\frac{\pi}{2}-\theta\right\)=\cos \theta) सह-फलन संबंध है। \(\frac{\pi}{2}\) वाले रूपांतरण में फलन बदलता है।
