Question

find the genral solution sin square x + cos x equals to 1 by 4​

Answer 1

Answer:

i don't know yar i know only english

Answer 2

$sin^2x + cosx = \frac{1}{4} \\\\4sin^2x + 4cosx = 1\\\\4 - 4cos^2x + 4cosx = 1\\\\4cos^2x - 4cosx -3 = 0\\\\4cos^2x-6cosx+2cosx-3 = 0\\\\2cosx(2cosx - 3) +1(2cosx-3) = 0\\\\(2cosx-3)(2cosx+1) = 0$

2cosx - 3 = 0          OR          2cosx + 1 = 0

cosx = 3/2              OR           cosx = -1/2

Since -1 ≤ cosx ≤ 1, cosx = 3/2 is rejected

So, cosx = -1/2

$cosx = -cos\frac{\pi }{3}\\ \\cosx = cos(\pi -\frac{\pi }{3})\\\\ cosx = cos\frac{2\pi }{3} \\\\ \huge\black\boxed{x= 2n\pi ± \frac{2\pi }{3}}$