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

Question

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

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Arya 1 month 2021-08-17T09:06:01+00:00 2 Answers 0 views 0

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    0
    2021-08-17T09:07:35+00:00

    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

    0
    2021-08-17T09:07:56+00:00

    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.

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