Question

Solve the equation 2cos^2x = sin2x , giving your answer in terms of π. 0

Answer 1

2cos^2x = sin2x 2cos^2x = 2sin x cos x (2sin x cos x) / (2cos^2x) = 1 sin x / cos x = 1 tan x = 1 x = π/4

Answer 2

Given is $2*cos^{2} (x)=sin(2x)$

We can use following formulas to solve this problem :-

1. $\frac{sin\;\theta}{cos\;\theta} = tan\;\theta$

2. sin(2∅) = 2·sin(∅)·cos(∅)

Solving the given equation :-

$2*cos^{2} (x)=sin(2x) \\\\2*cos^{2} (x)=2*sin(x)*cos(x) \\\\2*cos^{2} (x)-2*sin(x)*cos(x)=0 \\\\2*cos^{2}(x)*(1-\frac{sin(x)}{cos(x)}) =0 \\\\2*cos^{2}(x)*(1-tan(x)) =0 \\\\cos^{2}(x) = 0 \;or\; (1-tan(x)) =0 \\\\cos(x) = 0 \;or\; tan(x) =1 \\\\x = cos^{-1}(0) \;or\; x=tan^{-1}(1) \\\\x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4}$

Hence, final answer is $x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4}$.