Question

Ifsec theta+tantheta=1 prove sec theta=l^+1/2l

Answer 1

Answer:

$sec\theta=\frac{l^2+1}{2l}$

Step-by-step explanation:

Given:

$sec\theta+tan\theta=l$........(1)

We know that

$sec^2\theta-tan^2\theta=1$

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

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

$sec\theta-tan\theta=\frac{1}{l}$....(2)

Adding (1) and (2), we get

$sec\theta+tan\theta+sec\theta-tan\theta=l+\frac{1}{l}$

$2sec\theta=\frac{l^2+1}{l}$

$\implies\:sec\theta=\frac{l^2+1}{2l}$