Question

prove that 1-tan2A÷1+tan2A =1-2sin2A
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Answer 1

Step-by-step explanation:

1 - Tan²A / 1 + Tan²A = 1 - 2 sin²A

LHS = 1 - Tan²A / 1 + Tan²A

{TanA = sinA/cosA.... ( Tan²A = sin²A/cos²A) }

= 1 - sin²A/cos²A /1 + sin²A/cos²

{ 1/1 = 1... i.e. (sin²A/cos²A)/1 = sin²A/cos²A }

= 1 - sin²A/cos²A + sin²A/cos²A

{ a/b + c/d = a×d + c×b / b×d }

=1 - sin²A × cos²A + sin²A × cos²A / cos²A ×cos²A

{by Dividing Above- all cos²A Been cancelled}

= 1 - sin²A + sin²A

=1 - 2sin²A ---- { sin + sin = 2 sin } --------- 1

RHS= 1 - 2sin²A ----------------------- 2

:· by equations 1 and 2

RHS = LHS

:· 1-tan²A/ 1+tan²A = 1 - 2sin²A