If C O S E C X + Cot X = 11 2 , Then Tan X = - Mathematics

MCQ

If $cosec x + \cot x = \frac{11}{2}$, then tan x =

Options

• $\frac{21}{22}$

• $\frac{15}{16}$

• $\frac{44}{117}$

• $\frac{117}{44}$

Solution

$\frac{44}{117}$

We have:

$cosec x + \cot x = \frac{11}{2} \left( 1 \right)$

$\Rightarrow \frac{1}{cosecx + \cot x} = \frac{2}{11}$

$\Rightarrow \frac{{cosec}^2 x - \cot^2 x}{cosecx + \cot x} = \frac{2}{11}$

$\Rightarrow \frac{\left( cosec x + \cot x \right)\left( cosec x - \cot x \right)}{\left( cosec x + \cot x \right)} = \frac{2}{11}$

$\therefore cosec A-\cot x = \frac{2}{11} \left( 2 \right)$

Subtracting ( 2 ) from ( 1 ):

$2\cot x = \frac{11}{2} - \frac{2}{11}$

$\Rightarrow 2\cot x = \frac{121 - 4}{22}$

$\Rightarrow 2\cot x = \frac{117}{22}$

$\Rightarrow \cot x = \frac{117}{44}$

$\Rightarrow \frac{1}{\tan x} = \frac{117}{44}$

$\Rightarrow \tan x = \frac{44}{117}$

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 5 Trigonometric Functions
Q 13 | Page 42