Q166 / 270 · NDA 2013 (Phase 2) · Mathematics

What is $\sin ^2 20^{\circ}+\sin ^2 70^{\circ}$ equal to?

  • Correct answer
    A
    1
  • B
    0
  • C
    –1
  • D
    $\frac{1}{2}$

Solution

$\begin{aligned} & \sin ^2 20^{\circ}+\sin ^2 70^{\circ} \\ & \text {or, } \sin ^2 20^{\circ}+\sin ^2\left(90^{\circ}-20^{\circ}\right) \\ & \text {or, } \sin ^2 20^{\circ}+\cos ^2\left(20^{\circ}\right)=1 .\end{aligned}$

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

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