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If 7 sin2 θ + 3 cos2 θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ.

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This is an important question from the
Book- ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter- Trigonometric Identities
Chapter number-18

If 7 sin2 θ + 3 cos2 θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ

Trigonometric Identities, class 10th, chapter 18th, question no32 , ICSE board, ML aggarwal..

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1 Answer

  1. Given,

    7 sin2 θ + 3 cos2 θ = 4, 0° ≤ θ ≤ 90°

    3 sin2 θ + 3 cos2 θ + 4 sin2 θ = 4

    3 (sin2 θ + 3 cos2 θ) + 4 sin2 θ = 4

    3 (1) + 4 sin2 θ = 4

    4 sin2 θ = 4 – 3

    sin2 θ = ¼

    Taking square-root on both sides, we get

    sin θ = ½

    Thus, θ = 30o

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