Question

Prove that tan(45+∝)−tan(45−∝)/
tan(45+∝)+tan(45−∝)
=sin2∝

Answer 1

Answer:

tan (45+ a) = (1 + tan a)/ (1 – tana)

tan (45 – a) = (1 – tana)/ (1 + tana)

now use this in lhs

(1+ tana)^2 – (1 – tana)^2 / (1+tana)^2 + ( 1 – tan a)^2

= 4tana / 2 + 2 tan^2 a

= 2 tana /(1+tan2a)

= sin 2a