SOLUTION: I have to solve the following using trigonometric identities: 1-cos^2(x)*1-tan^2(x)=sin^2(x)-2sin^4(x)/ 1-sin^2(x) Using the trigonometric identities, I have to prove that it i

Question 611729: I have to solve the following using trigonometric identities:
1-cos^2(x)*1-tan^2(x)=sin^2(x)-2sin^4(x)/ 1-sin^2(x)
Using the trigonometric identities, I have to prove that it is one, preferably using the left-hand side.
I would appreciate any help that is given.
Thanks!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
1-cos^2(x)*1-tan^2(x)=sin^2(x)-2sin^4(x)/ 1-sin^2(x)
**
Starting with left side:
(1-cos^2x)(1-tan^2x)
=sin^2x(1-sin^2x/cos^2x)
=sin^2x[(cos^2x-sin^2x)/cos^2x]
=[sin^2x(1-sin^2x-sin^2x)]/(1-sin^2x)
=[sin^2x(1-2sin^2x)]/(1-sin^2x)
=sin^2x-2sin^4x)/(1-sin^2x)
verified:
left side=right side
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