# Trigonometric ratio Questions and answers

Topics

1). If $$\Large \sin \theta +cosec \theta =2,\ then\ \sin^{2} \theta + cosec^{2} \theta$$  is equal to
 A). 1 B). 4 C). 2 D). none of these
2). The value of $$\Large \frac{\cot^{2} \theta +1}{\cot^{2} \theta -1}$$ is equal to:
 A). $$\Large \sin 2 \theta$$ B). $$\Large \cos 2 \theta$$ C). $$\Large \cosh 2 \theta$$ D). $$\Large \sec 2 \theta$$
3). If $$\Large \tan A = 2 \tan B + \cot B,\ then\ 2 \tan \left(A-B\right)$$ is equal to:
 A). $$\Large \tan B$$ B). $$\Large 2 \tan B$$ C). $$\Large \cot B$$ D). $$\Large 2 \cot B$$
4). If $$\Large \tan A - \tan B = x\ and\ \cot B - \cot A = y,$$ then$$\Large \cot \left(A-B\right)$$ is equal to:
 A). $$\Large \frac{1}{x}+y$$ B). $$\Large \frac{1}{xy}$$ C). $$\Large \frac{1}{x}-\frac{1}{y}$$ D). $$\Large \frac{1}{x}+\frac{1}{y}$$
5). If $$\Large \sin \theta = -\frac{4}{5}\ and\ \theta$$ and $$\Large \theta$$ lies in the third quadrant, then $$\Large \cos \frac{ \theta }{2}$$ is equal to:
 A). $$\Large \frac{1}{\sqrt{5}}$$ B). $$\Large -\frac{1}{\sqrt{5}}$$ C). $$\Large \frac{2}{\sqrt{5}}$$ D). $$\Large -\frac{2}{\sqrt{5}}$$

6). The value of $$\Large \cos 1 ^{\circ} \cos 2 ^{\circ} \cos 3 ^{\circ} ....... \cos 100 ^{\circ}$$ is equal to:
 A). 1 B). -1 C). 0 D). none of these
7). The value of $$\Large \sin 12 ^{\circ} \sin 48 ^{\circ} \sin 54 ^{\circ}$$ is equal to:
 A). $$\Large \frac{1}{16}$$ B). $$\Large \frac{1}{32}$$ C). $$\Large \frac{1}{8}$$ D). $$\Large \frac{1}{4}$$
8). The value of $$\Large 2 cos\ x - \cos 3x - \cos 5x$$ is equal to
 A). $$\Large 16 \cos^{3} x \sin^{2} x$$ B). $$\Large 16 \sin^{3} x \cos^{2} x$$ C). $$\Large 4 \cos^{3} x \sin^{2} x$$ D). $$\Large 4 \sin^{3} x \cos^{2} x$$
9). If $$\Large \cos \theta = \frac{1}{2} \left(x+\frac{1}{x}\right),\ then\ \frac{1}{2} \left(x^{2} + \frac{1}{x^{2}}\right)$$ is equal to:
 A). $$\Large \sin 2 \theta$$ B). $$\Large \sec 2 \theta$$ C). $$\Large \tan 2 \theta$$ D). $$\Large \cos 2 \theta$$
10). The value of x for the maximum value $$\Large \sqrt{3} \cos x + \sin x$$ is:
 A). $$\Large 30 ^{\circ}$$ B). $$\Large 45 ^{\circ}$$ C). $$\Large 60 ^{\circ}$$ D). $$\Large 90 ^{\circ}$$
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