Question

Following question contains statements given in two columns, which have to be matched. The statements in $Column-I$ are labelled as A, B, C and D while the statements in $Column-II$ are labelled as p, q, r and s. Any given statement in $Column-I$ can have correct matching with $ONE$ statement in $Column-II$.

Answer 1

(A) $|\tan x|=\frac{m}{n}\Rightarrow \tan x=\frac{m}{n}$ & $\tan x=-\frac{m}{n}$
In $[0,2\pi ]$it has 4 solutions
(B) $\cos x+\cos 2x+\cos 3x+\cos 4x+\cos 5x=5$
$\Rightarrow \cos x=\cos 2x=\cos 3x=\cos 4x=\cos 5x=1$
$\Rightarrow x=2n_1\pi ,x=n_2\pi$,
$x=2n_3\frac{\pi }{3},x=\frac{n_4\pi }{2},x=\frac{2n_5\pi }{5}$
$\Rightarrow x=0,2\pi$ are common solutions.
(C) $\frac{1}{2^{1-|\cos x|}}=4$
$\Rightarrow \frac{1}{1-|\cos x|}=2\Rightarrow 1-|\cos x|=\frac{1}{2}$
$\Rightarrow |\cos x|=\frac{1}{2}\Rightarrow \cos x=\pm \frac{1}{2}$
$\therefore$ In $(-\pi ,\pi )$ there are 4 solutions
(D) $\tan \theta +\tan 2\theta +\tan 3\theta =\tan \theta \tan 2\theta \tan 3\theta$
$\Rightarrow \theta +2\theta +3\theta =n\pi \Rightarrow \theta =n\pi /6$
$\Rightarrow \theta =\frac{\pi }{3},\frac{2\pi }{3}$ satisfy equation only.