Question : If $x=a\cos\theta + b\sin\theta$ and $y=b\cos\theta-a\sin\theta$, then $x^{2}+y^{2}$ is equal to:

Option 1: $ab$

Option 2: $a^2+b^2$

Option 3: $a^2-b^2$

Option 4: $1$

Question : If $x\sin^{3}\theta +y\cos^{3}\theta=\sin\theta\cos\theta$ and $x\sin\theta-y\cos\theta=0$, then the value of $\left ( x^{2}+y^{2} \right )$ equals:

Option 1: $1$

Option 2: $\frac{1}{2}$

Option 3: $\frac{3}2$

Option 4: $2$

Question : If $x=a(\sin\theta+\cos\theta), y=b(\sin\theta-\cos\theta)$, then the value of $\frac{x^2}{a^2}+\frac{y^2}{b^2}$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –2

Question : If $x=8(\sin \theta+\cos \theta)$ and $y=9(\sin \theta-\cos \theta)$, then the value of $\frac{x^2}{8^2}+\frac{y^2}{9^2}$ is:

Option 1: 4

Option 2: 6

Option 3: 8

Option 4: 2

Question : If $x+\frac{1}{x}=2 \cos \theta$, then $x^3+\frac{1}{x^3}=?$

Option 1: $2 \cos 2θ$

Option 2: $\cos 3θ$

Option 3: $2 \cos 3θ$

Option 4: $\cos 2θ$

Question : If $\sin \theta+\sin ^2 \theta=1$, then the value of $\cos ^2 \theta+\cos ^4 \theta$ is equal to:

Option 1: 5

Option 2: $\frac{1}{2}$

Option 3: $1$

Option 4: $0$