3 years ago

2tan(45-A)/1+tan^2(45-A)=cos2a

Mathematics

1 answer:

AVprozaik [17]3 years ago

3 0

Answer:

Let θ = (45 - A)°.

=> 2Tanθ/ 1 + Tan²θ

=> 2Sinθ/Cosθ / 1 + Sin²θ / Cos²θ

=> 2Sinθ/Cosθ/ Cos²θ + Cos²θ / Cos²θ

=> 2Sinθ/Cosθ/ 1 / Cos²θ

=> 2SinθCos²θ/Cosθ

=> 2SinθCosθ

=> Sin2θ

But we assumed θ = (45 - A)°,

=> Sin2(45 - A)

=> Sin(90 - 2A) (∵ Sin(90 - θ) = Cosθ)

=> Cos2A

= R.H.S

Hence proved.

Step-by-step explanation:

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