Question

If `sqrt(2)` sec θ + tan θ = 1, then the general value of θ is

पर्याय

• `npi + (3pi)/4`

• `2npi + pi/4`

• `2npi - pi/4`

• `2npi +- pi/4`

Answer 1

`2npi - pi/4`

Explanation:

`sqrt(2)` sec θ + tan θ = 1

⇒ `sqrt(2)/cos theta + sin theta/cos theta` = 1

⇒ `sin theta - cos theta = - sqrt(2)`

Dividing by `sqrt(2)` on both sides, we get

`1/sqrt(2) sin theta - 1/sqrt(2) cos theta` = – 1

⇒ `1/sqrt(2) cos theta - 1/sqrt(2) sin theta` = 1

⇒ `cos(theta + pi/4)` = cos (0)

⇒ `theta + pi/4 = 2npi +- 0`

⇒ θ = `2npi - pi/4`.