SOLUTION: Can you please help me solve this trigonometric identities question: 1)Prove the following identities. a) {{{sin^2 (x) - cos^2 (x) = 2sin^2 (x) - 1}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Can you please help me solve this trigonometric identities question: 1)Prove the following identities. a) {{{sin^2 (x) - cos^2 (x) = 2sin^2 (x) - 1}}}       Log On


   

Question 204705: Can you please help me solve this trigonometric identities question: 1)Prove the following identities.
a) sin%5E2+%28x%29+-+cos%5E2+%28x%29+=+2sin%5E2+%28x%29+-+1
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
there is an identity formula of trigonometry :
sin%5E2+%28x%29+%2B+cos%5E2+%28x%29+=+1

by using that formula:
cos%5E2+%28x%29+=+1+-+sin%5E2+%28x%29

so:
sin%5E2+%28x%29+-+cos%5E2+%28x%29+=+sin%5E2+%28x%29+-+%281+-+sin%5E2+%28x%29%29
= sin%5E2+%28x%29+-+1+%2B+sin%5E2+%28x%29
= 2sin%5E2+%28x%29+-+1