Q177 / 270 · NDA 2012 (Phase 1) · Mathematics

Let $\sin (A+B)=1$ and $\sin (A-B)=1 / 2$, where $A, B$ $\in\left[0, \frac{\pi}{2}\right]$. What is $\sin ^2 \mathrm{~A}-\sin ^2 \mathrm{~B}$ equal to?

  • A
    0
  • Correct answer
    B
    1/2
  • C
    1
  • D
    2

Solution

$\begin{aligned} & \sin ^2 60^{\circ}-\sin ^2 30^{\circ} \\ & \frac{3}{4}-\frac{1}{4}=\frac{1}{2} .\end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions