Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 171-180 of 350 questions.
What is (\tan\(\frac{\pi}{2}+x\)) equal to?
A. \(-\cot x\)
\(\frac{\pi}{2}+x\) पर \(\tan\) बदलकर \(\cot\) होता है और चिन्ह ऋणात्मक होता है। इसलिए (\tan\(\frac{\pi}{2}+x\)=-\cot x)। / At \(\frac{\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{\pi}{2}+x\)=-\cot x).
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What is (\sec\(\frac{\pi}{2}-x\)) equal to?
C. \(\cosec x\)
(\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। / (\cos\(\frac{\pi}{2}-x\)=\sin x), so (\sec\(\frac{\pi}{2}-x\)=\frac{1}{\sin x}=\cosec x). Complementary angles give cofunctions.
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What is (\cosec\(\frac{\pi}{2}-x\)) equal to?
A. \(\sec x\)
(\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। / (\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.
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If (x) is in the second quadrant and \(\sin x=\frac{7}{25}\), what is the value of \(\cos x\)?
C. \(-\frac{24}{25}\)
पहचान से \(|\cos x|=\frac{24}{25}\) मिलता है। दूसरे चतुर्थांश में \(\cos x\) ऋणात्मक होता है। / The identity gives \(|\cos x|=\frac{24}{25}\). In the second quadrant, \(\cos x\) is negative.
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If (x) is in the third quadrant and \(\tan x=\frac{9}{40}\), what is the value of \(\sec x\)?
B. \(-\frac{41}{40}\)
\(\sec^2 x=1+\tan^2 x\) से \(|\sec x|=\frac{41}{40}\) मिलता है। तीसरे चतुर्थांश में \(\sec x\) ऋणात्मक होता है। / From \(\sec^2 x=1+\tan^2 x\), \(|\sec x|=\frac{41}{40}\). In the third quadrant, \(\sec x\) is negative.
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If (x) is in the fourth quadrant and \(\cos x=\frac{15}{17}\), what is the value of \(\sin x\)?
C. \(-\frac{8}{17}\)
पहचान से \(|\sin x|=\frac{8}{17}\) मिलता है। चौथे चतुर्थांश में \(\sin x\) ऋणात्मक होता है। / The identity gives \(|\sin x|=\frac{8}{17}\). In the fourth quadrant, \(\sin x\) is negative.
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If (x) is in the second quadrant and \(\cot x=-\frac{3}{4}\), what is the value of \(\cosec x\)?
A. \(\frac{5}{4}\)
\(\cosec^2 x=1+\cot^2 x\) से \(|\cosec x|=\frac{5}{4}\) मिलता है। दूसरे चतुर्थांश में \(\cosec x\) धनात्मक होता है। / From \(\cosec^2 x=1+\cot^2 x\), \(|\cosec x|=\frac{5}{4}\). In the second quadrant, \(\cosec x\) is positive.
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What is the simplified value of \(\frac{\sec^2 x-1}{\tan^2 x}\)?
A. \(1\)
त्रिकोणमितीय सर्वसमिका \(\sec^2 x=1+\tan^2 x\) से \(\sec^2 x-1=\tan^2 x\) मिलता है। अतः \(\frac{\sec^2 x-1}{\tan^2 x}=\frac{\tan^2 x}{\tan^2 x}=1\), जहाँ दिया गया व्यंजक परिभाषित है। \(0\) विकल्प गलत है, क्योंकि अंश और हर समान हैं, अंश शून्य होने पर हर भी शून्य होगा और भिन्न परिभाषित नहीं होगा। परीक्षा टिप: \(\sec^2 x-1\) दिखते ही उसे \(\tan^2 x\) से बदलें। / Using the identity \(\sec^2 x=1+\tan^2 x\), we get \(\sec^2 x-1=\tan^2 x\). Therefore, \(\frac{\sec^2 x-1}{\tan^2 x}=\frac{\tan^2 x}{\tan^2 x}=1\), wherever the given expression is defined. Option \(0\) is incorrect because the numerator and denominator are equal; when they are zero, the fraction is undefined rather than zero. Exam tip: Replace \(\sec^2 x-1\) directly with \(\tan^2 x\).
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What is the simplified value of \(\frac{\cosec^2 x-1}{\cot^2 x}\)?
C. 1
पाइथागोरसीय त्रिकोणमितीय सर्वसमिका \(\cosec^2 x=1+\cot^2 x\) से \(\cosec^2 x-1=\cot^2 x\) मिलता है। अतः \(\frac{\cosec^2 x-1}{\cot^2 x}=\frac{\cot^2 x}{\cot^2 x}=1\), जहाँ व्यंजक परिभाषित है। \(\cot^2 x\) उत्तर नहीं है, क्योंकि यह केवल अंश का सरल रूप है। परीक्षा टिप: \(\cosec^2 x=1+\cot^2 x\) को \(\sec^2 x=1+\tan^2 x\) के साथ याद रखें। / Using the Pythagorean trigonometric identity \(\cosec^2 x=1+\cot^2 x\), we get \(\cosec^2 x-1=\cot^2 x\). Therefore, \(\frac{\cosec^2 x-1}{\cot^2 x}=\frac{\cot^2 x}{\cot^2 x}=1\), wherever the expression is defined. \(\cot^2 x\) is not the final answer because it is only the simplified numerator. Exam tip: remember \(\cosec^2 x=1+\cot^2 x\) alongside \(\sec^2 x=1+\tan^2 x\).
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Which of the following trigonometric functions is an even function?
B. \(\cos x\)
\(\cos(-x)=\cos x\) होने के कारण \(\cos x\) सम फलन है। जबकि \(\sin(-x)=-\sin x\), इसलिए \(\sin x\), \(\tan x\) और \(\cot x\) विषम हैं। परीक्षा में \(f(-x)\) लिखकर पहचान करें। / Since \(\cos(-x)=\cos x\), \(\cos x\) is an even function. In contrast, \(\sin(-x)=-\sin x\), so \(\sin x\), \(\tan x\), and \(\cot x\) are odd. Exam tip: test parity by replacing \(x\) with \(-x\).
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