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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(0 \leq \theta \leq 2 \pi, 0 \leq \alpha \leq 2 \pi\) and \(\sec ^{2018} \theta\) \(+\operatorname{cosec}^{2018} \alpha=2\), then the value of \(\cos ^{2020} \theta+\sin ^{2022} \alpha=\)

  1. A \(\frac{3}{2}\)
  2. B \(\frac{1}{2^{2020}}\)
  3. C 1
  4. D 2
Verified Solution

Answer & Solution

Correct Answer

(D) 2

Step-by-step Solution

Detailed explanation

\(\sec ^{2018} \theta+\operatorname{cosec}^{2018} \alpha=2\) It is true for \(\theta=0\) and \(\alpha=\pi / 2\) \[ \begin{aligned} \therefore \cos ^{2020} \theta+\sin ^{2022} \alpha & =\cos ^{2020} 0+\sin ^{2022} \frac{\pi}{2} \\ & =1+1=2 \end{aligned} \]