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Solve the trigonometric equation: 4 3 theta = theta for all possible values of theta.

May 10, 2026Mathematics

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Step-by-step solution

3 steps

Here are the solutions for the given trigonometric equations:

(i) $4 \cos^3 \theta = \cos \theta$

Rearrange the equation to set it to zero.
$4 \cos^3 \theta - \cos \theta = 0$
Factor out $\cos \theta$ .
$\cos \theta (4 \cos^2 \theta - 1) = 0$
Set each factor equal to zero and solve for $\theta$ .
Case 1: $\cos \theta = 0$
$\theta = \frac{\pi}{2} + n\pi$
Case 2:

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