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
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Correct Answer: 0
Solution : $\sin 25^{\circ} \sin 65^{\circ}-\cos 25^{\circ} \cos 65^{\circ}$ We know that, $\cos(x + y) = \cos x \cos y - \sin x \sin y$ Applying, $\sin 25^{\circ} \sin 65^{\circ}-\cos 25^{\circ} \cos 65^{\circ}$ = $-(-\sin 25^{\circ} \sin 65^{\circ}+\cos 25^{\circ} \cos 65^{\circ})$ = $-\cos(25^{\circ}+65^{\circ})$ = $-\cos90^{\circ}=0$ Hence, the correct answer is 0.
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Question : Evaluate the following. $\sin 25° \sin 65° – \cos 25° \cos 65°$
Option 1: 4
Option 2: 1
Option 4: 40
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
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: $\cos \left(36^{\circ}+A\right) \cdot \cos \left(36^{\circ}-A\right)+\cos \left(54^{\circ}+A\right) \cdot \cos \left(54^{\circ}-A\right)$
Option 1: $\sin 2A$
Option 2: $\cos A$
Option 3: $\sin A$
Option 4: $\cos 2A$
Question : Find the value of $\sin^2 25^\circ+\sin^2 65^\circ$:
Option 1: $-1$
Option 2: $\frac{1}{2}$
Option 3: $0$
Option 4: $1$
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