Question 23

If $$ \tan \theta = \frac{1}{\sqrt{5}} $$ , find the value of $$ cosec^{2} \theta - \sec^{2}\theta $$

Solution

$$ \tan \theta = \frac{1}{\sqrt{5}} $$

Using identities like , 1 + $$\tan^2\theta = \sec^2\theta , 1 +\cot^2\theta = cosec^2\theta$$

$$ \sec^2\theta = \frac{6}{5} and cosec^2\theta = 6$$

Required answer = $$\frac{24}{5}$$

So , the answer would be option b)$$\frac{24}{5}$$.

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