Question

If $\sec \theta +\tan \theta =x$, obtain the values of $\sec \theta ,\tan \theta$ and $\sin \theta$.

Answer 1

Given $sec\theta +tan\theta =x$

As $1+ta{n}^2\theta =se{c}^2\theta$

$se{c}^2\theta -ta{n}^2\theta =1$

$(sec\theta -tan\theta )(sec\theta +tan\theta )=1$

$(sec\theta -tan\theta )x=1$

$sec\theta -tan\theta =1/x$

$sec\theta +tan\theta =x$

$sec\theta -tan\theta =1/x$

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$2sec\theta =x+\frac{1}{x}$