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Question: If cos<sup>–1</sup>\(\left( \frac{1}{x} \right)\) = q, then tan q=...

If cos–1(1x)\left( \frac{1}{x} \right) = q, then tan q=

A

1x2−1\frac{1}{\sqrt{x^{2} - 1}}

B

x2+1\sqrt{x^{2} + 1}

C

1−x2\sqrt{1 - x^{2}}

D

x2−1\sqrt{x^{2} - 1}

Answer

x2−1\sqrt{x^{2} - 1}

Explanation

Solution

Let cos–1 x = q. Then x = cos q

Ž tan q =sec⁡2θ−1\sqrt{\sec^{2}\theta - 1} = 1/x2−1\sqrt{x^{2} - 1} = 1−x2\sqrt{1 - x^{2}}/x