(D) Given $\sin(\theta) + \operatorname{cosec}(\theta) = 2$. Since $\operatorname{cosec}(\theta) = \frac{1}{\sin(\theta)}$,we have $\sin(\theta) + \fr

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(D) Given $\sin(\theta) + \operatorname{cosec}(\theta) = 2$. Since $\operatorname{cosec}(\theta) = \frac{1}{\sin(\theta)}$,we have $\sin(\theta) + \frac{1}{\sin(\theta)} = 2$. Let $x = \sin(\theta)$,then $x + \frac{1}{x} = 2$,which implies $x^2 - 2x + 1 = 0$,so $(x - 1)^2 = 0$. Thus,$\sin(\theta) = 1$. Therefore,$\sin^{2020}(\theta) + \operatorname{cosec}^{2020}(\theta) = (1)^{2020} + (1)^{2020} = 1 + 1 = 2$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Mix Examples-Trigonometrical Ratios, Functions and Identities

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If $\sin(\theta) + \operatorname{cosec}(\theta) = 2$,then $\sin^{2020}(\theta) + \operatorname{cosec}^{2020}(\theta) = \dots$

AP EAMCET 2020 All AP EAMCET

A
$2^{2020}$
B
$2020^{2019}$
C
$2^{2019}$
D
$2$

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