Question

prove that 2tan(45°-a)/1+tan²(45°-a)=cos2a

Answer 1

Answer:

Step-by-step explanation:

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.

Answer 2

Answer:

Step-by-step explanation: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 PROVED