Question

Use the identity tan(x) = sin(x) / cos(x) in the left hand side of the given identity. 
tan2(x) - sin2(x) = sin2(x) / cos2(x) - sin2(x) 
= [ sin2(x) - cos2(x) sin2(x) ] / cos2(x) 
= sin2(x) [ 1 - cos2(x) ] / cos2(x) 
= sin2(x) sin2(x) / cos2(x) 
= sin2(x) tan2(x) which is equal to the right hand side of the given identity.


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Answer 1

Explanation:

Use the identity tan(x) = sin(x) / cos(x) in the left hand side of the given identity.

tan2(x) - sin2(x) = sin2(x) / cos2(x) - sin2(x)

= [ sin2(x) - cos2(x) sin2(x) ] / cos2(x)

= sin2(x) [ 1 - cos2(x) ] / cos2(x)

= sin2(x) sin2(x) / cos2(x)

= sin2(x) tan2(x

Answer 2

tan2(x) - sin2(x) = sin2(x) / cos2(x) - sin2(x) 

= [ sin2(x) - cos2(x) sin2(x) ] / cos2(x) 

= sin2(x) [ 1 - cos2(x) ] / cos2(x) 

= sin2(x) sin2(x) / cos2(x) 

= sin2(x) tan2(x) which is equal to the right hand side of the given identity.