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 311-320 of 346 questions.
What is the product form of \(\cos 4x-\cos 2x\)?
B. \(-2\sin 3x\sin x\)
सूत्र \(\cos A-\cos B=-2\sin\frac{A+B}{2}\sin\frac{A-B}{2}\) है। इसलिए उत्तर \(-2\sin 3x\sin x\) है। / The formula is \(\cos A-\cos B=-2\sin\frac{A+B}{2}\sin\frac{A-B}{2}\). Hence the answer is \(-2\sin 3x\sin x\).
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What is the fundamental period of (f(x)=|\sin x|)?
D. \( \pi \)
\(|\sin x|\) में ऋणात्मक भाग धनात्मक हो जाता है, इसलिए पैटर्न हर \(\pi\) पर दोहरता है। परीक्षा में modulus से आवर्त घट सकता है। / In \(|\sin x|\), the negative part becomes positive, so the pattern repeats every \(\pi\). In exams, modulus can reduce the period.
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What is the fundamental period of (f(x)=\sin-2 x)?
A. \( \pi \)
क्योंकि (\sin-2\(x+\pi\)=\sin-2 x), इसलिए मूल आवर्त \(\pi\) है। परीक्षा में वर्ग वाले sine और cosine का आवर्त याद रखें। / Since (\sin-2\(x+\pi\)=\sin-2 x), the fundamental period is \(\pi\). In exams, remember the period of squared sine and cosine.
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If \(\sec x+\tan x=3\), what is the value of \(\sec x-\tan x\)?
B. \( \frac{1}{3} \)
क्योंकि (\(\sec x+\tan x\)\(\sec x-\tan x\)=1), इसलिए दूसरा गुणक \(\frac{1}{3}\) है। परीक्षा में reciprocal pair पहचानें। / Since (\(\sec x+\tan x\)\(\sec x-\tan x\)=1), the other factor is \(\frac{1}{3}\). In exams, identify reciprocal pairs.
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What is \(\frac{\sin 2x}{1+\cos 2x}\) equal to?
C. \(\tan x\)
\(\sin 2x=2\sin x\cos x\) और \(1+\cos 2x=2\cos^2 x\) रखें। परिणाम \(\tan x\) है। / Use \(\sin 2x=2\sin x\cos x\) and \(1+\cos 2x=2\cos^2 x\). The result is \(\tan x\).
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What is \(\frac{1-\cos 2x}{\sin 2x}\) equal to?
D. \(\tan x\)
\(1-\cos 2x=2\sin^2 x\) और \(\sin 2x=2\sin x\cos x\) लगाएं। सरलीकरण से \(\tan x\) मिलता है। / Use \(1-\cos 2x=2\sin^2 x\) and \(\sin 2x=2\sin x\cos x\). Simplification gives \(\tan x\).
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What is \(1+\tan^2 x\) equal to?
A. \(\sec^2 x\)
मूल पहचान \(1+\tan^2 x=\sec^2 x\) है। परीक्षा में इसे \(\sin^2 x+\cos^2 x=1\) से भी सिद्ध किया जा सकता है। / The basic identity is \(1+\tan^2 x=\sec^2 x\). In exams, it can also be derived from \(\sin^2 x+\cos^2 x=1\).
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If \(\cot x=3\), what is the value of \(\cosec^2 x\)?
B. (10)
\(\cosec^2 x=1+\cot^2 x\) होता है। इसलिए (1+9=10) है। / We know \(\cosec^2 x=1+\cot^2 x\). Hence (1+9=10).
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What is the value of \(\sin 75^\circ\cos 15^\circ-\cos 75^\circ\sin 15^\circ\)?
D. \( \frac{\sqrt{3}}{2} \)
यह (\sin\(75^\circ-15^\circ\)) का रूप है। इसलिए मान \(\sin 60^\circ=\frac{\sqrt{3}}{2}\) है। / This is the form of (\sin\(75^\circ-15^\circ\)). Hence the value is \(\sin 60^\circ=\frac{\sqrt{3}}{2}\).
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What is the value of \(\cos 80^\circ\cos 20^\circ+\sin 80^\circ\sin 20^\circ\)?
A. \( \frac{1}{2} \)
यह (\cos\(80^\circ-20^\circ\)) है। इसलिए मान \(\cos 60^\circ=\frac{1}{2}\) है। / This is (\cos\(80^\circ-20^\circ\)). Hence the value is \(\cos 60^\circ=\frac{1}{2}\).
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