Question

If sinθ = `1/sqrt(2)` and `π/2 < θ < π`. Then the value of `(sinθ + cosθ)/tanθ` is ______.

Options

• 0

• 1

• `1/sqrt(2)`

• `sqrt(2)`

Answer 1

If sinθ = `1/sqrt(2)` and `π/2 < θ < π`. Then the value of `(sinθ + cosθ)/tanθ` is 0.

Explanation:

sinθ = `1/sqrt(2)` and `π/2 < θ < π`

then θ = `π - π/4 = (3π)/4`

So `(sinθ + cosθ)/tanθ = (sin  (3π)/4 + cos  (3π)/4)/(tan  (3π)/4)`

= `(1/sqrt(2) - 1/sqrt(2))/(-1)`

= 0