(B) Given equations are: $\tan \theta + \sin \theta = a$ $(1)$ $\tan \theta - \sin \theta = b$ $(2)$ Adding $(1)$ and $(2)$: $2 \tan \theta = a + b$ $

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(B) Given equations are: $\tan \theta + \sin \theta = a$ $(1)$ $\tan \theta - \sin \theta = b$ $(2)$ Adding $(1)$ and $(2)$: $2 \tan \theta = a + b$ $\Rightarrow \tan \theta = \frac{a+b}{2}$ $\Rightarrow \cot \theta = \frac{2}{a+b}$ Subtracting $(2)$ from $(1)$: $2 \sin \theta = a - b$ $\Rightarrow \sin \theta = \frac{a-b}{2}$ $\Rightarrow \operatorname{cosec} \theta = \frac{2}{a-b}$ Thus,the values are $\frac{2}{a+b}$ and $\frac{2}{a-b}$.

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

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If $\tan \theta + \sin \theta = a$ and $\tan \theta - \sin \theta = b$,then the values of $\cot \theta$ and $\operatorname{cosec} \theta$ are respectively

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A
$\frac{1}{a+b}, \frac{1}{a-b}$
B
$\frac{2}{a+b}, \frac{2}{a-b}$
C
$\frac{2}{a-b}, \frac{2}{a+b}$
D
$\frac{1}{a-b}, \frac{1}{a+b}$

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If $\tan \theta + \sin \theta = a$ and $\tan \theta - \sin \theta = b$,then the values of $\cot \theta$ and $\operatorname{cosec} \theta$ are respectively

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