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Rajan@2021
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If 1+sin²θ = 3sinθcosθ then prove that tanθ = 1 or 1/2

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This question is taken from RS Aggarwal book, Trigonometry, topic – trigonometric identities and we have to prove that tanθ = 1 or 1/2

and we have given 1+sin²θ = 3sinθcosθ

Class 10, chapter 13A, question no 38.

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1 Answer

  1. 1+sin²θ = 3sinθcosθ

    Divide by cos²θ both sides, we get
    1/cos²θ + sin²θ/cos²θ = 3sinθ/cosθ
    sec²θ+tan²θ = 3tanθ

    1+tan²θ+tan²θ = 3tanθ        ( By Identity — sec²θ = 1+tan²θ)

    1+2tan²θ = 3tanθ

    Now let tanθ=a

    1+2=3a
    or   23a+1=0
    (2a1)(a1)=0

    By solving, we get
    a=1/2or1
    Thus, tanθ=1or1/2

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