Question

Prove that tan²teta-1 by
tan²teta +1
= =1-2cos² tete​

Answer 1

Here LHS =

tan²∅-1

tan²∅+1

sin²∅ - 1

= cos²∅

sin²∅ +1

cos²∅

sin²∅-cos²∅

cos²∅

= sin²∅+cos ²∅

cos²∅

= sin²∅-cos²∅

sin²∅+cos²∅

= (1-cos²∅)-cos²∅

1

= 1-cos²∅-cos²∅

= 1-2cos²∅

Applied formulas

tan∅= sin∅/cos∅

sin²∅+cos²∅=1

or

cos²∅= 1-sin²∅

or

sin²∅= 1-cos²∅