Question : What is the value of $\frac{\tan 45^{\circ}-\tan 15^{\circ}}{1+\tan 45^{\circ} \tan 15^{\circ}}$?

Option 1: $\sqrt{3}$

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

Option 3: $\frac{1}{\sqrt{3}}$

Option 4: ${\sqrt{2}}$

Question : Using trigonometric formulas, find the value of $(\frac{\sin (x-y)}{\sin (x+y)})(\frac{\tan x+\tan y}{\tan x-\tan y})$

Option 1: –2

Option 2: 2

Option 3: 0

Option 4: 1

Question : If $\frac{3–5x}{2x}+\frac{3–5y}{2y}+\frac{3–5z}{2z}=0$, the value of $\frac{2}{x}+\frac{2}{y}+\frac{2}{z}$ is:

Option 1: 20

Option 2: 5

Option 3: 10

Option 4: 15

Question : The value of $\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ}$ is ______.

Option 1: 4

Option 2: 3

Option 3: 1

Option 4: 2

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: $–2$