If 1/4 is a solution of Sin2x=pCosx, then p is? (a) -3 (b) 0 (c) 1 (d) -1 I think option (b) is correct, but I want solution.

Dec 28, 2016

$p = 0.4948$

Explanation:

$\sin 2 x = p \cos x$

$\Leftrightarrow 2 \sin x \cos x = p \cos x$

or $\cos x \left(2 \sin x - p\right) = 0$

i.e. either $\cos x = 0 \Rightarrow x = \left(2 n + 1\right) \frac{\pi}{2}$, where $n$ is an integer - but this does not give us a value of $p$, as $\frac{1}{4}$ is not among possible values.

or $2 \sin x - p = 0$ i.e. $p = 2 \sin x$

as $\frac{1}{4}$ is a solution, we have $2 \sin \left(\frac{1}{4}\right) - p = 0$ or $p = 2 \sin \left(\frac{1}{4}\right)$

(assuming that $\frac{1}{4}$ as solution is in radians)

$p = 2 \times 0.2474 = 0.4948$