Test Index

Trigonometric Equations

Section: Mathematics

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Question : 10 of 24

Marks: +1, -0

The number of solutions of the equation

2 \sin^2 \theta - 3 \cos^2 \theta = \sin \theta \cos \theta

lying in the interval

(-\pi, \pi)

[AP EAPCET 21 May 2025 S1]

2
4
3
1

Solution:

We have,

2 \sin^2 \theta - 3 \cos^2 \theta = \sin \theta \cos \theta

Dividing both sides by

\cos^2 \theta

, we get

\cos \theta \neq 0

\;\Rightarrow\;\; 2 \tan^2 \theta - 3 = \tan \theta

\;\Rightarrow\;\; 2 \tan^2 \theta - \tan \theta - 3 = 0

\;\Rightarrow\;\; (2 \tan \theta - 3)(\tan \theta + 1) = 0

\;\because\;\; \tan \theta = \frac{3}{2} \; \text{and} \; \tan \theta = -1

Clearly, in the interval

(-\pi, \pi) \tan \theta = \frac{3}{2}

gives two solution and

\tan \theta = -1

gives two solution

\therefore

Total number of solution

=4

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