If tan x = (sin θ + cos θ)/(sin θ − cos θ), π/4

Question

If tan x = (sin θ + cos θ)/(sin θ − cos θ), π/4 < θ < π/2, then what is √2 sin x equal to?

Accepted Answer

sin θ + cos θ. tan x = (sinθ+cosθ)/(sinθ−cosθ). Then sin x = (sinθ+cosθ)/√((sinθ+cosθ)²+(sinθ−cosθ)²) = (sinθ+cosθ)/√2. So √2 sin x = sin θ + cos θ.

If tan x = (sin θ + cos θ)/(sin θ − cos θ), π/4 < θ < π/2, then what is √2 sin x equal to?