Question

Show that (cos^2Φ + tan^2Φ - 1) / sin^2Φ = tan^2Φ..

Answer 1

Here i used θ as angle
i)cos^2θ=1-sin^2θ
ii)tan^2θ=sin^2θ/cos^2θ
iii)-1+sec^2θ=tan^2θ

Lhs =(cos^2θ+tan^2 θ-1)/sin^2θ

=(1-sin^2θ+tan^2θ-1)/sin^2θ
=(-sin^2θ+tan^2θ)/sin^2θ

=-sin^2θ/sin^2θ + tan^2θ/sin^2θ

=-1+(sin^2θ/cos^2θ)(1/sin^2θ)
=-1 +1/cos^2θ
=-1+sec^2θ
=tan^2θ
=Rhs