SOLUTION: Prove the identity. (Hint: factor the left side first) {{{ 2sec^2(theta)tan^2(theta)-tan^4(theta)=sec^4(theta)-1 }}} Thanks my friends.

Algebra ->  Trigonometry-basics -> SOLUTION: Prove the identity. (Hint: factor the left side first) {{{ 2sec^2(theta)tan^2(theta)-tan^4(theta)=sec^4(theta)-1 }}} Thanks my friends.      Log On


   

Question 1101708: Prove the identity. (Hint: factor the left side first)
+2sec%5E2%28theta%29tan%5E2%28theta%29-tan%5E4%28theta%29=sec%5E4%28theta%29-1+
Thanks my friends.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+2sec%5E2%28theta%29tan%5E2%28theta%29-tan%5E4%28theta%29=sec%5E4%28theta%29-1+
----
Multiply thru by cos^2
+2tan%5E2%28t%29-sin%5E4%28t%29%2Fcos%5E2%28t%29+=+sec%5E2%28t%29-+cos%5E2%28t%29+
Multiply thru by cos^2 again
+2sin%5E2%28t%29-sin%5E4%28t%29+=+1-+cos%5E4%28t%29+
+2sin%5E2%28t%29+-+1+=+sin%5E4%28t%29+-+cos%5E4%28t%29

+2sin%5E2%28t%29+-+1+=+sin%5E2%28t%29+-+cos%5E2%28t%29
+2sin%5E2%28t%29+-+sin%5E2%28t%29+-+cos%5E2%28t%29+=+sin%5E2%28t%29+-+cos%5E2%28t%29
sin%5E2%28t%29+-+cos%5E2%28t%29+=+sin%5E2%28t%29+-+cos%5E2%28t%29