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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Correct Answer: $1$
Solution : Given: $\sin^2 25^\circ+\sin^2 65^\circ$ $= \sin^2 25^\circ+\sin^2 (90^\circ – 65^\circ)$ $= \sin^2 25^\circ+\cos^2 25^\circ=1$ Hence, the correct answer is $1$.
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Question : Evaluate the following. $\sin 25^{\circ} \sin 65^{\circ}-\cos 25^{\circ} \cos 65^{\circ}$.
Question : Find the value of $\frac{\cos^2 15^{\circ}-\sin^2 15^{\circ}}{\cos^2 145^{\circ}+\sin^2 145^{\circ}}$.
Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?
Question : Find the value of $\cos 47^\circ \sec 133^\circ + \sin 44^\circ \text{cosec}\; 136^\circ $.
Question : What is the value of $\frac{\cos 37^{\circ}}{\sin 53^{\circ}}?$
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