How to solve cos^2x=1-sinx

Answer 1

Hi Christian P.,

It is always a good idea to reduce the number of functions operating within an equation. Here, the trig identity cos^2 (x) = 1 - sin^2 (x) is useful as a substitution.

So you end up with 1 - s^2(x) = 1 - s(x)

This has the form of a^2 = a , or a=1

so if sin(x) = 1 (or more exactly, -sin^2(x) = -sin(x)), you should be able to solve, right? (Watch your signs!!)

-- Cheers, -- Mr. d.

Answer 2

Hi Christian P.,

It is always a good idea to reduce the number of functions operating within an equation. Here, the trig identity cos^2 (x) = 1 - sin^2 (x) is useful as a substitution.

So you end up with 1 - s^2(x) = 1 - s(x)

This has the form of a^2 = a , or a=1

so if sin(x) = 1 (or more exactly, -sin^2(x) = -sin(x)), you should be able to solve, right? (Watch your signs!!)

-- Cheers, -- Mr. d.

Answer 3

cos² x = 1 - sin x

1 - sin² x = 1 - sin x

sin² x = sin x

sin² x - sin x = 0

sin x (sin x - 1) = 0

x ∈ {0, π/2, π}