SOLUTION: how to verify the identity of problem tan^2(x)-sin^2(x)=sin^4(x)sec^2(x)

Question 410609: how to verify the identity of problem
tan^2(x)-sin^2(x)=sin^4(x)sec^2(x)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
how to verify the identity of problem
tan^2(x)-sin^2(x)=sin^4(x)sec^2(x)
..
tan^2(x)-sin^2(x)=sin^4(x)sec^2(x)
starting with the right-hand side,
sin^4(x)sec^2(x)
=(sin^2)(sin^2)(1/cos^2)
=(sin^2/cos^2)*sin^2
=tan^2*sin^2
=tan^2*(1-cos^2)
=tan^2-tan^2*cos^2
=tan^2-(sin^2/cos^2)*cos^2
=tan^2-sin^2
verified: right-hand side=left-hand side
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