Thread: Prove the Trig Identity

Prove the trig identity.

tan 70 = 2tan50 + tan20

Originally Posted by magentarita

Prove the trig identity.

tan 70 = 2tan50 + tan20

2tan 50+tan 20=(tan 20+tan 50)+tan 50.....1
tan(50+20)=tan50+tan20/1-tan20.tan50
tan70(1-tan20.tan50)=tan50+tan20......2
now by comparing 1&2 we have 2tan 50+tan 20=tan70(1-tan20.tan50)+tan50
=tan70-tan20.tan50.tan70+tan50 as (tan70=cot20) we have
tan70-tan50+tan50=tan70

Originally Posted by euclid2

2tan 50+tan 20=(tan 20+tan 50)+tan 50.....1
tan(50+20)=tan50+tan20/1-tan20.tan50
tan70(1-tan20.tan50)=tan50+tan20......2
now by comparing 1&2 we have 2tan 50+tan 20=tan70(1-tan20.tan50)+tan50
=tan70-tan20.tan50.tan70+tan50 as (tan70=cot20) we have
tan70-tan50+tan50=tan70

This is a tough one.