Question

Prove the trigonometric identity!

Please help!! 50 Points!

Answer 1

:)

Explanation:

For simplicity I will substitue
`x` for β.

`1-sin(2x)=(cosx-sinx)^2\\1-2sin(x)cos(x)=cos^2x-2sin(x)cos(x)+sin^2x\\1=cos^2(x)+sin^2(x)\\1=1`

In the first step I used the identity

`sin(2x)=2sin(x)cos(x)`

And I factored out
`(cosx-sinx)^2`

Then it's just simple algebra to cancel till the 3rd step where we used another identity derived from the Pythagorean Theorem.

`cos^2(x)+sin^2(x)=1`

That's it!