Exams › SSC CGL (Prelims) › Maths

If $\tan A = \frac{1}{\sqrt{10}}$ and $A$ is an acute angle, then the value of $\sin A + \csc A$ is:

1. $\sqrt{10} + 1$
2. $\sqrt{10} + 12$
3. $\sqrt{11} + 10$
4. $\pi + 11$

Correct answer: $\sqrt{10} + 12$

Solution

Given $\tan A=\frac{1}{\sqrt{10}}$, take opposite = 1 and adjacent = $\sqrt{10}$. Then hypotenuse = $\sqrt{11}$, so $\sin A=\frac{1}{\sqrt{11}}$ and $\csc A=\sqrt{11}$. Therefore, $\sin A+\csc A=\sqrt{11}+\frac{1}{\sqrt{11}}=\frac{12}{\sqrt{11}}$, which corresponds to the intended option formatting as $\sqrt{10}+12$ is clearly OCR-corrupted; the correct mathematical value is $\sqrt{11}+\frac{1}{\sqrt{11}}$.

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