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Question: If \(x = \sec\theta + \tan\theta,\) then \(x + \frac{1}{x} =\)...

If x=sec⁡θ+tan⁡θ,x = \sec\theta + \tan\theta, then x+1x=x + \frac{1}{x} =

A

1

B

2sec⁡θ2\sec\theta

C

2

D

2tan⁡θ2\tan\theta

Answer

2sec⁡θ2\sec\theta

Explanation

Solution

Given that x=sec⁡θ+tan⁡θx = \sec\theta + \tan\theta

⇒x+1x=sec⁡θ+tan⁡θ+1sec⁡θ+tan⁡θ\Rightarrow x + \frac{1}{x} = \sec\theta + \tan\theta + \frac{1}{\sec\theta + \tan\theta}

=sec⁡θ+tan⁡θ+sec⁡θ−tan⁡θ=2sec⁡θ= \sec\theta + \tan\theta + \sec\theta - \tan\theta = 2\sec\theta