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 \(\cos ^{2020} \theta+\sin ^{2022} \alpha=\)
- A \(\frac{3}{2}\)
- B \(\frac{1}{2^{2020}}\)
- C 1
- D 2
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 \(\alpha=\pi / 2\) \[ \begin{aligned} \therefore \cos ^{2020} \theta+\sin ^{2022} \alpha & =\cos ^{2020} 0+\sin ^{2022} \frac{\pi}{2} \\ & =1+1=2 \end{aligned} \]
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- In \(\triangle \mathrm{ABC}\), if a, b, c are in arithmetic progression and \(\mathrm{C}=2 \mathrm{~A}\), then \(\mathrm{a}: \mathrm{c}=\)AP EAMCET 2023 Medium
- Let If is independent of , then the relation between and isAP EAMCET 2019 Medium
- A straight line \(L\) cuts both the lines \(5 x-y-4=0\) and \(3 x+4 y-4=0\). The segment of \(L\) between the two lines is bisected at the point \((1,5)\). The equation of \(L\) isAP EAMCET 2017 Medium
- If \(I=\int_0^\pi x\left\{\sin ^2(\sin x)+\cos ^2(\cos x)\right\} d x\), then,
\([I]=\ldots .\). Here,[.] denotes greatest integer function.AP EAMCET 2021 Hard - If \(A=\left[\begin{array}{lll}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{array}\right]\) and \(\operatorname{det}\left(A^3\right)=125\), then \(x=\)AP EAMCET 2022 Easy
- If tangents are drawn from any point on the circle \(x^2+y^2=25\) to the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\), then the angle between the tangents isAP EAMCET 2014 Easy
More PYQs from AP EAMCET
- Which one of the following statements is not correct?AP EAMCET 2016 Easy
- An urn contains 3 black and 5 red balls. If 3 balis are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn isAP EAMCET 2024 Easy
- The chemicals and the reaction conditions required for the preparation of ethane areAP EAMCET 2005 Easy
- If \(35 \hat{\mathbf{i}}+14 \hat{\mathbf{j}}-77 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) and \(5 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}\) are coplanar, then \(\lambda\) is equal toAP EAMCET 2021 Medium
- The distance between the origin and the normal to the curve drawn at is_____ unitsAP EAMCET 2021 Medium
- If \(y=4 \cos ^3(t)\) and \(x=4 \sin ^3(t)\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2021 Medium