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

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Asked: March 16, 20212021-03-16T02:37:27+05:30 2021-03-16T02:37:27+05:30In: ICSE

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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AAREKH · Answer 1 · 2021-03-16T02:55:21+05:30

AAREKH Guru

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 = 30^o