solve Sin^2x+cosx=1?

Question

Sin^2x+cosx=1?

Answer 1

The equation is sin²(x) + cos(x) = 1.

[1 - cos²(x)] + cos(x) = 1    [∵ sin²(x) = 1 - cos²(x)]

- cos²(x) + cos(x) = 0

cos(x) [1 - cos(x)] = 0

cos(x) = 0 and  1 - cos(x) = 0

cosx = 0              (or)      cosx = 1

x = cos^-1(0)         (or)   x = cos^-1(1)

x = cos^-1(cos 90)  (or)      x = cos^-1(cos 0 )

x = 2nπ ± π/2      (or)      x = 2nπ

The solution are x = 2nπ ± π/2 and x = 2nπ ± 0.