Exams › SSC CGL (Prelims) › General

If $\tan A=\frac{1}{\sqrt{3}}$, what is the value of $(1-\sin A)(1+\cos A)$?

1. $(2+\sqrt{3})/4$
2. $(2-\sqrt{3})/4$
3. $(4+\sqrt{3})/4$
4. $(1+\sqrt{3})/4$

Correct answer: $(2+\sqrt{3})/4$

Solution

Since $\tan A=\frac{1}{\sqrt{3}}$, take $A=30^\circ$ in the first quadrant. Then $\sin A=\frac12$ and $\cos A=\frac{\sqrt3}{2}$, so $(1-\sin A)(1+\cos A)=\left(1-\frac12\right)\left(1+\frac{\sqrt3}{2}\right)=\frac{2+\sqrt3}{4}$.

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