Question

sinx+cosx=1/sinx

скажите решение пожалуйста!!!

 

Answer 1

$sin x + cos x = frac{1}{sin x} | * sin x, sin x ne 0\\ sin^2 x + sin x cos x = 1\\ sin^2 x + sin x cos x = sin^2 x + cos^2 x\\ sin x cos x - cos^2 x = 0\\ cos x (sin x - cos x) = 0\\ 1) cos x = 0, x = frac{pi}{2} + pi n, n in mathtt{Z}\\ 2) sin x - cos x = 0, sin x = cos x, x = frac{pi}{4} + pi n, n in mathtt{Z}$