One of the solutions of the equation 8 \sin^3 \theta -7 \sin \theta + 3 \cos \theta = 0 lies in the interval

Correct Answer is : (10°, 20°]

KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 14 of 120

Marks: +1, -0

One of the solutions of the equation

8 \sin^3 θ -7 \sin θ + 3 \cos θ = 0

lies in the interval

Solution:

6 \sinθ -2 \sin 3θ-7 \sinθ + 3 \cos θ= 0

√3 \cos θ- \sin θ = 2 \sin 3θ

It can be written as

2 (\sin (60º -θ)) = 2 \sin 3θ

\sin (60º-θ) = \sin 3θ

60º = 4θ
⇒ θ = 15º is one of the value

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