Доказать тождество tg t/ tgt + ctgt = sin*2 t

Question

Доказать тождество tg t/ tgt + ctgt = sin*2 t

Answer 1

[sint/cost]/[sint/cost +cost/sint] = sin²t

[sint/cost]/[(sint*sint + cost*cost)/cost*sint] = sin²t

[sint/cost]/[(sin²t+cos²t)/sint*cost] = sin²t

[sint/cost]/[1/sint*cost] = sin²t

sint/cost * sont*cost = sin²t

sint * sint = sin²t  

sin²t =  sin²t