Question

If `sec theta + tan theta = x,"  find the value of " sec theta`

Answer 1

We have , 

`sec theta + tan theta = x    ............(i)`

⇒ `(sec theta + tan theta )/1 xx (sec theta- tan theta )/(sec theta - tan theta ) = x`

`⇒  (sec ^2 theta - tan^2 theta )/( sec theta - tan theta) = x`

`⇒1/ (sec theta - tan theta ) = x/1`

`⇒ sec theta - tan theta = 1/x `              ............(ii)

𝐴𝑑𝑑𝑖𝑛𝑔 (𝑖)𝑎𝑛𝑑 (𝑖𝑖), 𝑤𝑒 𝑔𝑒𝑡

`2 sec theta = x+ 1/x`

⇒` 2 sec theta = (x^2+1)/x`

∴ `sec theta = (x^2 +1)/(2x)`