Question

Derive
cos2x=1-(tan)2x/1+(tan)2x

Answer 1

LHS,

We have,

cos 2x = cos²x - sin²x

= (cos²x - sin²x) / 1

= (cos²x - sin²x) / (cos²x + sin²x)

= {cos²x[1-(sin² x/cos² x)]} / {cos²x[1+(sin²x/cos²x)]}

⇒ cos2x = (1 - tan²x) / (1 + tan²x)  

= RHS

Hence Proved !!