Question

Question #185da

Answer 1

This identity is true for any value of `x in RR`, except where the denominators are zero.

Explanation:

Start by cross multiplying
`cos^2(x)=(1-sin(x))(1+sin(x))`

Factor the right hand side
`cos^2(x)=1+sin(x)-sin(x)-sin^2(x)`
`cos^2(x)=1-sin^2(x)`

Adding `sin^2(x)` both sides gives the identity
`sin^2(x)+cos^2(x)=1`

This identity is true for any value of `x` in the real numbers `RR`

However, recall that denominators cannot be zero, so the answer is all `RR` except wherever

`cos(x)=0`, so when `x=pi/2(2n-1)`, where `ninZZ`
and `sin(x)=1`, so when `x=pi/2(4n+1)`, where `ninZZ`