Question : What is the value of $\sin 75^{\circ}+\sin 15^{\circ}$?
Option 1: $\frac{1}{\sqrt{2}}$
Option 2: $\frac{\sqrt{3}}{2}$
Option 3: $\sqrt{\frac{3}{2}}$
Option 4: $\frac{3}{\sqrt{2}}$
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Correct Answer: $\sqrt{\frac{3}{2}}$
Solution : Let $t=\sin 15^\circ+\sin75^\circ$ Now, $t=\sin 15^\circ+\cos (90-75)^\circ$ $⇒t=\sin 15^\circ+\cos 15^\circ$ Squaring on both sides, we get, $t^2=\sin^2 15^\circ+\cos^2 15^\circ+2\sin15^\circ \cos15^\circ$ $⇒t^2=1+\sin 30^\circ$ $⇒t^2=1+\frac{1}{2}$ $\therefore t=\sqrt{\frac{3}{2}}$ Hence, the correct answer is $\sqrt{\frac{3}{2}}$.
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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 : What will be the value of $\sin 10^{\circ}- \frac{4 }{ 3} \sin ^3 10^{\circ}?$
Question : What is the value of $\frac{\tan 45^{\circ}-\tan 15^{\circ}}{1+\tan 45^{\circ} \tan 15^{\circ}}$?
Question : If $\theta=135^{\circ} ; y=15^{\circ}$, what is the value of $2\cos(\theta)\sin(y)$?
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