Question

2tantheta/1+tan^²theta+2tantheta/1-tan^²theta=2cos^²theta×tan2theta​

Answer 1

Answer:

Step-by-step explanation:

2Tanθ / 1 + Tan²θ  + 2Tanθ/ 1 - Tan²θ

=> [2(Sinθ/Cosθ) / 1 + (Sin²θ/Cos²θ) ] + Tan2θ  (∵2Tanθ/ 1 - Tan²θ = Tan2θ)

=> [2SinθCos²θ/Cosθ /Cos²θ + Sin² θ] + Tan2θ

=> Sin2θ + Tan2θ        (∵ Sin2θ = 2SinθCosθ)

=> Sin2θ + Sin2θ/Cos2θ

=> Sin2θ[ 1 + 1/Cos2θ]

=> Sin2θ [ Cos2θ + 1 / Cos2θ]

=> Sin2θ/Cos2θ ( 1 + Cos2θ)

=> Tan2θ * 2Cos²θ                (∵ Cos2θ = 2Cos²θ - 1)

= R.H.S

Hence proved