Question

If √(1-sin^2x=-cosx and √1-cos^2x=sinx then x lies in​

Answer 1

√1 - sin 2x = √sin^2x + cos^2x - 2 sinx.cosx

√1 - sin 2x = √ (sin x - cos x)^2 or √ (cos x - sin 2x)^2

Now , when the value of x lies from 0° to 30° or from 270° to 360° the value of cos is always greater than the value of sin then the root of 1 - sin 2x will be ( cos x- sin x ) ; when the value of x lies between 60° and 180° then the value of sin will be greater than the value of cos, then the root of 1 - sin 2x will be ( sin x - cos x ) and at 45° the root will be 0.

Hope that works. :)