Question 66

If $$\cosec 2 \theta = \sec (3 \theta - 15^\circ), then \theta $$ is equal to:

Solution

$$\cosec2\theta = \sec(3\theta - 15)$$

=$$ \sec(3\theta +90 - 105)$$

= $$\sec(90 - (-3\theta + 105)$$

{$$sec(90 - \theta) = cosec\theta$$}

$$\cosec2\theta = \cosec(-3\theta + 105)$$

$$2\theta = -3\theta + 105$$

$$\theta = 21$$

So , the answer would be option d)$$21^\circ$$.

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