(A) Given,$\sin \theta + \operatorname{cosec} \theta = 2$. We know that $\operatorname{cosec} \theta = \frac{1}{\sin \theta}$. So,$\sin \theta + \frac

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(A) Given,$\sin \theta + \operatorname{cosec} \theta = 2$. We know that $\operatorname{cosec} \theta = \frac{1}{\sin \theta}$. So,$\sin \theta + \frac{1}{\sin \theta} = 2$. Let $\sin \theta = x$,then $x + \frac{1}{x} = 2$,which implies $x^2 - 2x + 1 = 0$,or $(x - 1)^2 = 0$. Thus,$x = 1$,which means $\sin \theta = 1$. Consequently,$\operatorname{cosec} \theta = 1$. Therefore,$\sin^{10} \theta + \operatorname{cosec}^{10} \theta = (1)^{10} + (1)^{10} = 1 + 1 = 2$.

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 the value of $\sin^{10} \theta + \operatorname{cosec}^{10} \theta$ is equal to

AP EAMCET 2021 All AP EAMCET

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$2$
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$2^{10}$
C
$2^9$
D
$2^8$

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Mix Examples-Trigonometrical Ratios, Functions and Identities

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If $\sin \theta + \operatorname{cosec} \theta = 2$,then the value of $\sin^{10} \theta + \operatorname{cosec}^{10} \theta$ is equal to

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