Question

3. If sec theta+ tan theta =1/3 then sec theta =
1) 10/3
2) 5/3
3) 2/3
4) 1/6
​

Answer 1

$\sec( \alpha ) + \tan( \alpha ) = \frac{1}{3}$

$\frac{ (\sec\alpha + \tan \alpha ) ( \sec \alpha - \tan\alpha) } {( \sec \alpha - \tan\alpha) } = \frac{1}{3}$

$\frac{ {sec}^{2} \alpha - {tan}^{2} \alpha }{( \sec \alpha - \tan\alpha) } = \frac{1}{3}$

$\frac{1}{( \sec \alpha - \tan\alpha) } = \frac{1}{3}$

$\sec( \alpha ) - \tan( \alpha ) = 3$

Now. Add the first and last line

$2 \sec( \alpha ) = \frac{10}{3}$

$\sec( \alpha ) = \frac{5}{3}$