Q64 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Mathematics

$\cos ^2 45^{\circ}+\cos ^2 135^{\circ}+\cos ^2 225^{\circ}+\cos ^2 315^{\circ}=$

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

Solution

$\begin{aligned} & \cos ^2 45^{\circ}+\cos ^2 135^{\circ}+\cos ^2 225+\cos ^2 315^{\circ} \\ &=\cos ^2 45^{\circ}+\cos ^2\left(180^{\circ}-45^{\circ}\right)+\cos ^2\left(180^{\circ}+45^{\circ}\right) \\ &+\cos ^2\left(360^{\circ}-45^{\circ}\right) \\ &= 4 \cos ^2 45^{\circ}=4\left(\frac{1}{\sqrt{2}}\right)^2=2\end{aligned}$

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

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