Math, asked by bankiewmawlieh94, 5 months ago

tan2A=2 tanA/1- tan^ A

Answers

Answered by amritaSN04

2

Answer:

tanA = sinA/cosA

therefore,

tan (2A) = sin(2A) / cos(2A)

tan2A = 2 sinA*cosA ÷ (cos²A - sin²A)

Dividing both numerator and denominator by cos²A

= 2 (sinAcosA /cosA) ÷ [(cos²A/cos²A)-(sin²A/cos²A)]

= 2 (sinA/cosA) ÷ [(1- sin²A/cos²A)]

= 2 tanA ÷ [1- (sinA/cosA)²]

= 2tanA/1-tan²A

hence, proved

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