Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}+\sec 45^{\circ} × \sin 45^{\circ}}{\sec 60^{\circ}+{\text{cosec}} 30^{\circ}}$ is:
Option 1: $\frac{1}{4}$
Option 2: $-\frac{3}{8}$
Option 3: $\frac{3}{8}$
Option 4: $-\frac{1}{4}$
Correct Answer: $\frac{3}{8}$
Solution :
$\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}+\sec 45^{\circ} × \sin 45^{\circ}}{\sec 60^{\circ}+{\text{cosec}} 30^{\circ}}$
$=\frac{\frac{1}{2}^{2} + \frac{1}{2}^{2} + \sqrt 2 × \frac{1}{\sqrt 2}}{2 + 2}$
$=\frac{\frac{1}{4} + \frac{1}{4} + 1}{2 + 2}$
$=\frac{\frac{3}{2}}{4}$
$=\frac{3}{8}$
Hence, the correct answer is $\frac{3}{8}$.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
