Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If C O S E C X + C O T X = 11 2 , Then Tan X = - Mathematics

MCQ

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

 

Options

  • \[\frac{21}{22}\]

     

  • \[\frac{15}{16}\]

     

  • \[\frac{44}{117}\]

     

  • \[\frac{117}{43}\]

     

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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): 

\[2\cot x = \frac{11}{2} - \frac{2}{11}\]

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

\[ \Rightarrow 2\cot x = \frac{117}{22}\]

\[ \Rightarrow \cot x=\frac{117}{44}\]

\[ \Rightarrow \frac{1}{\tan x} = \frac{117}{44}\]

\[ \Rightarrow \tan x = \frac{44}{117}\]

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 5 Trigonometric Functions
Q 21 | Page 42
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