Question

If sec theta is equal to x + 1 by 4 x then prove that sec theta + tan theta is equal to 2x or 1 by 2x

Answer 1

Answer:

hope this will help!!!!

Answer 2

Explanation:

$\tan^2 \theta =\sec^2\theta -1 \\\\\tan^2 \theta =\left ( x+\frac{1}{4x} \right )^2-1\\\\=x^2+\frac{1}{16x^2}+2x(\frac{1}{4x})\\\\=x^2+\frac{1}{16x^2}-\frac{1}{2}\\\\\tan^2\theta=\left ( x-\frac{1}{4x} \right )^2\\\\\tan\theta = \pm \left (x- \frac{1}{4x} \right )$

when

$\tan\theta = + \left (x- \frac{1}{4x} \right )\\\\\sec\theta +\tan\theta\\\\x+\frac{1}{4x}+x-\frac{1}{4x}\\\\=2x$

when

$\tan\theta = - \left (x- \frac{1}{4x} \right )\\\\\sec\theta +\tan\theta\\\\x+\frac{1}{4x}-x+\frac{1}{4x}\\\\=\frac{1}{2x}$

hence proved

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