Question

Prove that
1+cot theta/sin theta + 1+tan theta/cos theta = cosec theta sec² theta+sec theta cosec² theta

(using LHS/RHS method)


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Answer 1

To prove:

(sinθ+cosecθ)2+(cosθ+secθ)2=7+tan2θ+cot2θ

Solution:

L.H.S. =(sinθ+cosecθ)2+(cosθ+secθ)2

=sin2θ+cosec2θ+2sinθ.cosecθ+cos2θ+sec2θ+2cosθ.secθ

=(sin2θ+cos2θ)+1+cot2θ+2+1+tan2θ+2

=1+6+tan2θ+cot2θ

=7+tan2θ+cot2θ

= R.H.S.