Question

If x y sin cos sin cos 3 3 θ θ θθ + = and x y sin cos θ θ = , than x y 2 2 + is equal to

Answer 1

The value of $x^{2}+y^{2}$ is equal to 1.

Step-by-step explanation:

We have,

$x=\sin 3\theta$        .......(1)

and,

$y=\cos 3\theta$       .......(2)

To find, the value of $x^{2} +y^{2} =?$

Squaring and adding (1) and (2), we get

$x^{2}+y^{2}=(\sin 3\theta)^{2} +(\cos 3\theta)^{2}$

⇒ $x^{2}+y^{2}=\sin^2 3\theta +\cos^2 3\theta$

⇒ $x^{2}+y^{2}=1$

[∵ $\sin^2 \theta +\cos^2 \theta=1$]

The value $x^{2}+y^{2}=1$

Hence, the value of $x^{2}+y^{2}$ is equal to 1.