Question : Evaluate the expression: $\frac{\sin ^2 63^{\circ}+\sin ^2 27^{\circ}}{\cos ^2 17^{\circ}+\cos ^2 73^{\circ}}$
Option 1: 0
Option 2: 3
Option 3: 1
Option 4: 2
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Correct Answer: 1
Solution : $\frac{\sin ^2 63^{\circ}+\sin ^2 27^{\circ}}{\cos ^2 17^{\circ}+\cos ^2 73^{\circ}}$ = $\frac{\sin ^2 63^{\circ}+\sin ^2 (90^{\circ}-63^{\circ})}{\cos ^2 17^{\circ}+\cos ^2 (90^{\circ}-17^{\circ})}$ = $\frac{\sin ^2 63^{\circ}+\cos ^2 63^{\circ}}{\cos ^2 17^{\circ}+\sin ^2 17^{\circ}}$ = $\frac{1}{1}$ = 1 Hence, the correct answer is 1.
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Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?
Option 1: $\frac{1}{\sqrt{2}}$
Option 2: $\sqrt{3}$
Option 3: $1$
Option 4: $\frac{1}{\sqrt{3}}$
Question : Evaluate the following. $\sin 25^{\circ} \sin 65^{\circ}-\cos 25^{\circ} \cos 65^{\circ}$.
Option 1: 40
Option 2: 4
Option 3: 0
Option 4: 1
Question : Find the value of $\frac{\cos^2 15^{\circ}-\sin^2 15^{\circ}}{\cos^2 145^{\circ}+\sin^2 145^{\circ}}$.
Option 1: $\frac{1}{\sqrt{3}}$
Option 2: $\frac{1}{1-\sqrt{3}}$
Option 3: $\frac{\sqrt{3}}{2}$
Option 4: $\frac{2}{\sqrt{3}}$
Question : $\sin 600^\circ \cos 750^\circ+\sin 150^\circ \cos 240^\circ=?$
Option 1: $\frac{2}{3}$
Option 2: $1$
Option 3: $\frac{1}{2}$
Option 4: $-1$
Question : $\frac{\cos 20^{\circ}}{\sin 70^{\circ}}+\frac{\cos \theta}{\sin \left(90^{\circ}-\theta\right)}=$_________,
Option 1: $-2$
Option 2: $\frac{1}{2}$
Option 3: $-\frac{1}{2}$
Option 4: $2$
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