Question

Prove the identitpls
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Answer 1

||✪✪ QUESTION ✪✪||

❦ prove that ( 1 - TanA/ 1 - cotA )² = Tan²A ?

|| ✰✰ ANSWER ✰✰ ||

➳ ( 1 - TanA/ 1 - cotA )²

Putting value of cotA = 1/TanA in Denominator we get,

➳ [ ( 1 - tanA) / ( 1 - 1/TanA) ]²

Taking LCM in Denominator now,

➳ [ ( 1 - tanA) / ( TanA - 1/TanA) ]²

➳ [ TanA( 1- tanA) / (TanA - 1) ]²

Taking (-1) common From Denominator now, we get,

➳ [ (-1)*TanA*( 1- tanA) / (1 - TanA) ]²

Now , (1 - TanA) will be cancel ,

➳ ( - TanA)²

➳ Tan²A = RHS

✪✪ Hence Proved ✪✪

Answer 2

QUESTION :-

=>> prove that ( 1 - TanA/ 1 - cotA )² = Tan²A ?

ANSWER :---

Taking LHS first

=> ( 1 - TanA/ 1 - cotA )²

Putting value of cotA = 1/TanA in Denominator we get,

=> [ ( 1 - tanA) / ( 1 - 1/TanA) ]²

Taking LCM in Denominator we get,

=> [ ( 1 - tanA) / ( TanA - 1/TanA) ]²

=> [ TanA( 1- tanA) / (TanA - 1) ]²

Taking (-1) common From Denominator now, we get,

=> [ (-1)*TanA*( 1- tanA) / (1 - TanA) ]²

Now , (1 - TanA) will be cancel ,

=> ( - TanA)²

=> Tan²A = RHS

❁❁ Hence Proved ❁❁