Q92 / 180 · COMEDK 2020 · Mathematics

$\sin ^{2} 175^{\circ}+\sin ^{2} 725^{\circ}$ is equal to

  • Correct answer
    A
    $\tan ^{2} 45^{\circ}$
  • B
    $\cos ^{2} 90^{\circ}$
  • C
    $\sin ^{2} 45^{\circ}$
  • D
    $\cos ^{2} 30^{\circ}$

Solution

We have, $\quad \sin ^{2} 17.5^{\circ}+\sin ^{2} 72.5^{\circ}=\sin ^{2} 17.5^{\circ}+\cos ^{2}\left(90^{\circ}-72.5^{\circ}\right)$ $=\sin ^{2} 175^{\circ}+\cos ^{2} 17.5^{\circ}=1=\tan ^{2} 45^{\circ}$

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

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