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

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(D) Given $\sin \theta + \text{cosec} \theta = 2$. Since $\text{cosec} \theta = \frac{1}{\sin \theta}$,we have $\sin \theta + \frac{1}{\sin \theta} = 2$. Multiplying by $\sin \theta$,we get $\sin^2 \theta + 1 = 2 \sin \theta$. This simplifies to $\sin^2 \theta - 2 \sin \theta + 1 = 0$,which is $(\sin \theta - 1)^2 = 0$. Thus,$\sin \theta = 1$. Therefore,$\sin^{10} \theta + \text{cosec}^{10} \theta = (1)^{10} + \frac{1}{(1)^{10}} = 1 + 1 = 2$.

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

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If $\sin \theta + \text{cosec} \theta = 2$,the value of $\sin^{10} \theta + \text{cosec}^{10} \theta$ is

A
$10$
B
$2^{10}$
C
$2^9$
D
$2$

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Trigonometrical Ratios, Functions and Identities

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Mix Examples-Trigonometrical Ratios, Functions and Identities

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