Question

Which double-angle or half-angle identity would you use to verify that

Answer 1

RTP: 1 + cos2x = 2/1+tan^2x

LHS = 1 + cos2x

= 1 + 2cos^2x - 1

= 2cos^2x

RHS = 2/1+tan^2x

= 2/sec^2x

= 2 x cos^2x

= 2cos^2x

2cos^2x=2cos^2x

LHS = RHS

Explanation:

Answer 2

RTP: 1 + cos2x = 2/1+tan^2x

LHS = 1 + cos2x
= 1 + 2cos^2x - 1
= 2cos^2x

RHS = 2/1+tan^2x
= 2/sec^2x
= 2 x cos^2x
= 2cos^2x

2cos^2x=2cos^2x
LHS = RHS