Question 60

If $$3x = \sec A$$ and $$\frac{3}{x}=\tan A$$ then $$\left(x^{2} - \frac{1}{x^{2}}\right)$$ is _____________.

Solution

This is a previous year paper question, the given answer is option c(1). But it is wrong.

Given $$3x=\sec A\ \Rightarrow x=\frac{\sec A}{3}$$

$$\frac{1}{x}=\frac{\tan A}{3}$$

$$\left(x^{2} - \frac{1}{x^{2}}\right)$$

On substituting the values of x and 1/x in the equation.

We know $$sec A^2-\tan A^2$$=1

$$\left(\left(\frac{\sec A}{3}\right)^2-\left(\frac{\tan A}{3}\right)^2\right)=\frac{1}{9}\left(\sec A^2-\tan A^2\right)=\frac{1}{9}$$

So, the answer is 1/9.

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