Question

2sec^2-sec^4-2cose^2+cosec^4=cot^4-tan^4 prove that

Answer 1

Answer:

2sec2x−sec4x−2cosec2x+cosec4x=cot4x−tan4x

LHS

2sec2x−sec4x−2cosec2x+cosec4x  

=cosec4x−2cosec2x−(sec4x−2sec2x)  

=cosec4x−2cosec2x−(sec4x−2sec2x+1)+1  

=cosec4x−2cosec2x+1−(sec4x−2sec2x+1)  

=(cosec4x−2cosec2x+1)−(sec4x−2sec2x+1)  

=(cosec2x−1)2−(sec2x−1)2  

=(cot2x)2−(tan2x)2  

=cot4x−tan4x  

= RHS

Hope this helps. Happy learning!!!