Question

How do you solve `2cosx=secx`?

Answer 1

x = 45° + k.180° or x = 135° + k.180°. k`epsilon`Z.

Explanation:

x cannot equal 90° + k.180°, k`epsilon`Z, sec x undefined.
multiply throughout by cos x
then 2 `cos^2 x` = 1
`cos^2 x` = `1/2`

hence cos x = ± `1/sqrt2`

Reference angle is 45°

cos x = `1/sqrt2`, when x = 45° or 315°
and cos x = 1`1/sqrt2`, when x = 135° or 225°
add multiples of 360° to each answer and combine to get final answer.