Question 64

For $$\theta$$ being an acute angle,it is given that, $$3(\cosec^2 \theta + \cot^2 \theta) = 5. Then \theta$$ is equal to:

Solution

$$3(\cosec^2 \theta + \cot^2 \theta) = 5$$

$$\left(1+\cot^2\theta\right)+\left(1+\cot^2\theta\right)+\left(1+\cot^2\theta\right)+3\cot^2\theta=5$$ $$((1+\cot^2\theta=\cosec^2 \theta))$$

$$3+3\cot^2\theta+3\cot^2\theta=5$$

$$\cot^2\theta=\frac{1}{3}$$

$$\cot\theta=\frac{1}{\sqrt{3}}$$

$$\theta=60^{\circ}$$

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