How do you prove trig identity?

Favorite Answer

first:let's use u = x/2 ( to simplify the writing
tan(u)( 2cot(2u)+ tan(u))

now, cot (2u) = 1/tan(2u) and tan(2u) = 2tan(u)/(1 - tan^2(u))
so cot (2u) = (1-tan^2(u))/2 tan(u)
so...

tan(u)( 2cot(2u)+ tan(u))
= tan(u) (2(1-tan^2(u))/2tan(u) + tan(u))
=tan(u) (1 - tan^2(u)/tan(u) + tan(u))
= 1 - tan^2(u) + tan^2(u)
= 1
Q.E.D....Show more

tan(x/2)(2cotx + tan(x/2))

=> tan(x/2)(2[1 - tan^2(x/2)]/2tan(x/2) + tan(x/2))

=> tan(x/2)([1 - tan^2(x/2)]/tan(x/2) + tan(x/2))

=> [1 - tan^2(x/2)] + tan^2(x/2))

=> 1...Show more