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।
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।
