Question : What is the value of $\sin 28° \sin 35° \sin 45° \sec 62° \sec 55°$?
Option 1: $2$
Option 2: $\frac{1}{\sqrt{2}}$
Option 3: $\sqrt{2}$
Option 4: $\frac{1}2$
Correct Answer: $\frac{1}{\sqrt{2}}$
Solution :
Given expression is $\sin 28° \sin 35° \sin 45° \sec 62° \sec 55°$.
We know, $\sin \theta = \cos(90°-\theta)$
So, $\sin 28° = \cos(90° - 28°)$ = $\cos 62°$
Also, $\sin 35° = \cos(90° - 35°)$ = $\cos 55°$
Substituting these values in the given expression, we get
$\sin 28° \sin 35° \sin 45° \sec 62° \sec 55°$
= $\cos 62° \cos 55° \sin 45° \sec 62° \sec 55°$
= $\sin 45°$ (Since, $\sec \theta \cos \theta = 1$)
= $\frac{1}{\sqrt{2}}$
Hence, the correct answer is $\frac{1}{\sqrt{2}}$.
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