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  4. If x= sec θ+ tan θ, then x+(1/x)=

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Q. If $x=\sec \theta+\tan \theta$, then $x+\frac{1}{x}=$

Trigonometric Functions

Solution:

Given that, $x=\sec \theta+\tan \theta$
$\Rightarrow x+\frac{1}{x}=\sec \,\theta+\tan \,\theta+\frac{1}{\sec\, \theta+\tan\, \theta}$
$=\sec \,\theta+\tan\, \theta+\sec \,\theta-\tan\, \theta=2 \sec \,\theta$