Question

Prove: tan 70° = tan 20° + 2tan 50°

Answer 1

As we all know,
According to the trigonometric identity,
tan70=tan(20+50)
tan70=(tan20+tan50)/1-tan20tan50
tan70-tan20tan50tan70=tan20+tan50
Also tan70tan20=tan70cot70=1
Hence
tan70-tan50=tan20+tan50
So tan70=tan20+2tan50
Hope this helps :) :)

Answer 2

tan(70-20)=tan50
 tan70-tan20/1+tan20 tan70=tan50
 tan20 tan70=cot70 tan70=1
 tan70-tan20/2=tan50
 tan70-tan20=2tan50
 tan70=tan20+2tan50