Prove that sec^2Q-cos^2Q = sin^2Q(sec^2Q+1)
Answers
Answered by
1
Step-by-step explanation:
Take LHS, sec^2Q-cos^2Q
=1/cos^2Q-cos^2Q
=1-cos^4Q/cos^2Q
=(1+cos^2Q)(1-cos^2Q)/cos^2Q
=(1+cos^2Q)(sin^2Q)/cos^2Q
=(1+cos^2Q)*tan^2Q
=tan^2Q+sin^2Q.
Take RHS,sin^2Q(sec^2Q+1)
=sin^2Q(1/cos^2Q+1)
=sin^2Q/cos^2Q+sin^2Q
=tan^2Q+sin^2Q.
LHS=RHS.
Thus proved.
Similar questions