167k views
22 votes
Prove the trigonometric identity!

Please help!! 50 Points!

Prove the trigonometric identity! Please help!! 50 Points!-example-1
User RobinL
by
4.5k points

1 Answer

9 votes

Answer:

:)

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!

User Diego Borba
by
4.7k points