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

Question

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

Options

\[\frac{21}{22}\]
\[\frac{15}{16}\]
\[\frac{44}{117}\]
\[\frac{117}{43}\]

MCQ

Solution

\[\frac{44}{117}\]

We have:

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

\[ \Rightarrow \frac{1}{cosec x + \cot x} = \frac{2}{11}\]

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

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

\[ \therefore cosecx-\cot x = \frac{2}{11} \left( 2 \right)\]

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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Trigonometric Equations

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Q 21 Q 20 Q 22

Chapter 5: Trigonometric Functions - Exercise 5.5 [Page 42]

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RD Sharma Mathematics [English] Class 11

Chapter 5 Trigonometric Functions
Exercise 5.5 | Q 21 | Page 42

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