If π2<θ<π, then write the value of √2+√2+2 cos 2 θ in the simplest form.
Since π2<θ<π
⇒ θ lies in the 2nd quadrant
Now,
√2±√2+2 cos 2 θ=√2±√2(1+cos 2θ)=√2±√2.2 cos2 θ=√2−(2 cos θ)
(∵ θ lies in the 2nd quadrant)
=√2(1−cos θ)=2.2 sin2 θ2=2 sin θ2