Question : If $\frac{\cos \theta}{(1+\sin \theta)}+\frac{\cos \theta}{(1-\sin \theta)}=4$ and $\theta$ is acute, then the value of $\theta$ is:
Option 1: $60^{\circ}$
Option 2: $15^{\circ}$
Option 3: $45^{\circ}$
Option 4: $30^{\circ}$
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Correct Answer: $60^{\circ}$
Solution :
$\frac{\cos \theta}{(1+\sin \theta)}+\frac{\cos \theta}{(1-\sin \theta)}=4$
Multiplying the two fractions by $(1+\sin \theta)(1-\sin \theta)=\cos^2 \theta$.
$⇒ \cos \theta (1-\sin \theta) + \cos \theta (1+\sin \theta) = 4 \cos^2 \theta$
$⇒ 2 \cos \theta = 4 \cos^2 \theta$
$⇒ 1 = 2 \cos \theta$
$⇒ \cos \theta = \frac{1}{2}$
$⇒ \theta = 60^\circ$
Hence, the correct answer is $60^\circ$.
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