Question

Cos theta + sin theta - sin 2 theta = 1/2 , 0 < theta < π/2

Answer 1

Answer:

θ= π/3 or π/6

Step-by-step explanation:

We are given that, Cosθ+Sinθ-Sin2θ = 1/2 .......... (1)

Now we have to solve for θ from the above relation, where 0< θ <π/2.

We can write from equation (1) that

Cosθ+Sinθ-Sin2θ = 1/2

⇒ Sinθ - Sin2θ = $\frac{1}{2}$ - Cosθ

⇒ Sinθ - 2SinθCosθ = ( 1 - 2Cosθ)/2

⇒ Sinθ (1-2Cosθ) = (1-2Cosθ)/2

⇒ (1-2Cosθ)(Sinθ-1/2)=0

So, from the above relation we can conclude that

Either, (1-2Cosθ)=0 or, (Sinθ-1/2)=0

⇒ Cosθ=1/2 or, Sinθ =1/2

Therefore, θ= π/3 or π/6. {Since,  0 < θ < π/2}

(Answer)