Question #297e2

2 Answers
Nov 2, 2016

Both sides equals sin^2t-cos^2t

Explanation:

(tan^2t-1)/sec^2t=(sin^2t/cos^2t-1)/(1/cos^2t)=sin^2t-cos^2t

(tant-cott)/(tant+cott)=(sint/cost-cost/sint)/(sint/cost+cost/sint)=((sin^2-cos^2t)/(sintcost))/((sin^2+cos^2t)/(sintcost))=sin^2t-cos^2t

Nov 6, 2016

LHS=(tan^2T-1)/sec^2T

=(tan^2T-1)/(1+tan^2T)

[Dividing numerator and denominator by tanT ]

=(tan^2T/tanT-1/tanT)/(1/tanT+tan^2T/tanT)

=(tanT-cotT)/(cotT+tanT)=RHS

Proved