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 331-340 of 346 questions.
What is \(2\sin x\cos x\) equal to?
B. \(\sin 2x\)
दुगुना कोण सूत्र के अनुसार \(2\sin x\cos x=\sin 2x\)। परीक्षा में यह identity बार-बार काम आती है। / By the double angle formula, \(2\sin x\cos x=\sin 2x\). This identity is used frequently in exams.
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What is \(\cos^2 x-\sin^2 x\) equal to?
C. \(\cos 2x\)
दुगुना कोण पहचान \(\cos 2x=\cos^2 x-\sin^2 x\) है। परीक्षा में \(\cos 2x\) के तीनों रूप याद रखें। / The double angle identity is \(\cos 2x=\cos^2 x-\sin^2 x\). In exams, remember all three forms of \(\cos 2x\).
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If \(\sin x-\cos x=1\), what is the value of \(\sin x\cos x\)?
A. (0)
दोनों ओर वर्ग करने पर \(1-2\sin x\cos x=1\) मिलता है। इसलिए \(\sin x\cos x=0\)। / Squaring both sides gives \(1-2\sin x\cos x=1\). Hence \(\sin x\cos x=0\).
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What is \(\tan x+\cot x\) equal to?
A. \( \sec x\cosec x \)
\(\tan x+\cot x=\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}\) है। सरलीकरण से \(\frac{1}{\sin x\cos x}=\sec x\cosec x\) मिलता है। / We have \(\tan x+\cot x=\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}\). Simplifying gives \(\frac{1}{\sin x\cos x}=\sec x\cosec x\).
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What is the fundamental period of (f(x)=\tan 3x)?
B. \( \frac{\pi}{3} \)
\(\tan ax\) का आवर्त \( \frac{\pi}{|a|} \) होता है। यहाँ (a=3), इसलिए आवर्त \( \frac{\pi}{3} \) है। / The period of \(\tan ax\) is \( \frac{\pi}{|a|} \). Here (a=3), so the period is \( \frac{\pi}{3} \).
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What is the period of (f(x)=\cos 4x)?
C. \( \frac{\pi}{2} \)
\(\cos ax\) का आवर्त \( \frac{2\pi}{|a|} \) होता है। इसलिए \(\cos 4x\) का आवर्त \( \frac{\pi}{2} \) है। / The period of \(\cos ax\) is \( \frac{2\pi}{|a|} \). Hence the period of \(\cos 4x\) is \( \frac{\pi}{2} \).
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If (x) is in the second quadrant and \(\sin x=\frac{5}{13}\), what will \(\cos x\) be?
D. \(-\frac{12}{13} \)
द्वितीय चतुर्थांश में \(\cos x\) ऋणात्मक होता है। \(\sin^2 x+\cos^2 x=1\) से \(\cos x=-\frac{12}{13}\)। / In the second quadrant, \(\cos x\) is negative. From \(\sin^2 x+\cos^2 x=1\), \(\cos x=-\frac{12}{13}\).
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If (x) lies in the third quadrant and \(\tan x=\frac{4}{3}\), what is \(\sin x\)?
A. \(-\frac{4}{5} \)
तृतीय चतुर्थांश में \(\sin x\) और \(\cos x\) दोनों ऋणात्मक होते हैं, पर \(\tan x\) धनात्मक होता है। इसलिए \(\sin x=-\frac{4}{5}\)। / In the third quadrant, both \(\sin x\) and \(\cos x\) are negative, while \(\tan x\) is positive. Hence \(\sin x=-\frac{4}{5}\).
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Which is the correct expansion of \(\sin 3x\)?
B. \(3\sin x-4\sin^3 x\)
त्रिगुण कोण सूत्र \(\sin 3x=3\sin x-4\sin^3 x\) है। परीक्षा में sign की गलती न करें। / The triple angle formula is \(\sin 3x=3\sin x-4\sin^3 x\). In exams, avoid sign mistakes.
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Which is the correct expansion of \(\cos 3x\)?
C. \(4\cos^3 x-3\cos x\)
त्रिगुण कोण सूत्र \(\cos 3x=4\cos^3 x-3\cos x\) है। परीक्षा में इसे \(\sin 3x\) से confuse न करें। / The triple angle formula is \(\cos 3x=4\cos^3 x-3\cos x\). In exams, do not confuse it with \(\sin 3x\).
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