Question : If $\tan x = \frac{7}{5}$, the value of $\frac{9 \sin  x – \frac{42}{5} \cos x}{15 \sin x + 21 \cos x}$ is:

Option 1: 0

Option 2: 1

Option 3: 0.1

Option 4: 0.5

Question : If $x\sin ^{2}60^{\circ}-\frac{3}{2}\sec 60^{\circ}\tan^{2}30^{\circ}+\frac{4}{5}\sin ^{2}45^{\circ}\tan ^{2}60^{\circ}=0$, then $x$ is:

Option 1: $-\frac{1}{15}$

Option 2: $–4$

Option 3: $-\frac{4}{15}$

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 $x+y+z=0$, then what is the value of $\frac{x^2}{(y z)}+\frac{y^2}{(x z)}+\frac{z^2}{(x y)}$?

Option 1: 1

Option 2: 0

Option 3: 2

Option 4: 3

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: $2$