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Question 73
If $$2 \cos^2 \theta - 5 \cos \theta + 2 = 0, 0^\circ < \theta < 90^\circ$$, then the value of $$(\cosec \theta + \cot \theta)$$ is:
Solution
we have $$2\cos^2\theta\ -5\cos\theta\ +2\ =0$$
By solving the above equation, we get $$\cos\theta\ =\frac{1}{2}$$
$$\theta\ =60$$
now $$\operatorname{cosec}60+\cot60=\frac{2}{\sqrt{\ 3}}+\frac{1}{\sqrt{\ 3}}$$
$$=\frac{3}{\sqrt{\ 3}}\ =\ \sqrt{\ 3}$$
Hence Option A is correct.
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