Question

prove that tan(a+b)(tan(a-b)tan2a=tan2a-tan(a+b)-tan(a-b)

Answer 1

We can write as
Tan2a=tan[(a+b) +(a-b)]
The value will be same
Now using formula
tan2a=tan(a+b) +tan(a-b) /1-tan(a+b). tan(a-b)
After multiply
tan2a-tan(a+b). tan(a-b). tan2a=tan(a+b)+tan(a-b)
U can write as
tan(a+b). tan(a-b). tan2a=tan2a-tan(a+b) -tan(a-b)
Hence proved
Hope it will help you