If `sec theta + tan theta = k, cos theta` equals to

Options

A. `(k^(2) +1)/(2k)`
B. `(2k)/(k^(2)+1)`
C. `k/(k^(2)+1)`
D. `k/(k^(2) -1)`

Answer

B

Explanation

`sec theta + tan theta = k`
` (sec^(2) theta - tan^(2) theta)/( sec theta -tan theta) = k`
` sec theta - tan theta = 1/k`
On adding Eqs. (i) and (ii) we get
` 2 sec theta = k + 1/k = (k^(2) +1)/k`
` Rightarrow cos theta = (2k)/( k^(2) +1)`