Question

sec^4theta-2sec²theta tan^2theta+tan^4theta/cosec^4theta-2cosec^2thetacot^2theta+cot^4theta=1​

Answer 1

Answer:

Statement : 2sec2x−sec4x−2cosec2x+cosec4x=cot4x−tan4x2sec2x−sec4x−2cosec2x+cosec4x=cot4x−tan4⁡x

LHS

2sec2x−sec4x−2cosec2x+cosec4x2sec2x−sec4x−2cosec2x+cosec4x

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

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

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

=rhs