Question

Prove the trigonometric identity! Please help!! 50 Points!

Answer 1

Answer:

:)

Step-by-step 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!