math Solve in R sinx1cos2xSolutionWe have to solve sin x 1

math

Solve in R sinx=1+cos^2x

Solution

We have to solve sin x = 1 + (cos x)^2

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

sin x = 1 + (cos x)^2

=> sin x = 1 + 1 - (sin x)^2

=> (sin x)^2 + sin x - 2 = 0

=> (sin x)^2 + 2*sin x - sin x - 2 = 0

=> (sin x)(sin x + 2) - 1(sin x + 2) = 0

=> (sin x - 1)(sin x + 2) = 0

=> sin x = 1 and sin x = -2

But sin x cannot be less than -1, we eliminate this root.

sin x = 1

x = pi/2 + 2*n*pi

The values of x are pi/2 + 2*n*pi