Question

verify identity of 1+cos2a = 2/ 1+tan^2a

Answer 1

by
(1) cos(2a) = cos²(a) - sin²(a) ,
(2) sin²(a) + cos²(a) = 1 ,
(3) tan²(a) + 1 = sec²(a) .
Using (1) and (2) we get
1 + cos(2a) = 1 + cos²(a) - sin²(a) = 2 cos²(a) .
cos²(a) = 1 / sec²(a) and applying (3), we find
2 cos²(a) = 2 / sec²(a) = 2 / (1 + tan²(a)