# The Value of 2 Tan π 10 + 3 Sec π 10 − 4 Cos π 10 is - Mathematics

MCQ

The value of  $2 \tan \frac{\pi}{10} + 3 \sec \frac{\pi}{10} - 4 \cos \frac{\pi}{10}$ is

#### Options

• 0

• $\sqrt{5}$

• 1

• none of these

#### Solution

$\text{ We have } ,$
$2\tan\frac{\pi}{10} + 3\sec\frac{\pi}{10} - 4\cos\frac{\pi}{10}$
$= 2\tan18° + 3\sec18° - 4\cos18°$
$= 2\frac{\sin18° }{\cos18° } + 3 \times \frac{1}{\cos18° } - 4\cos18°$
$= 2 \times \frac{\frac{\sqrt{5} - 1}{4}}{\frac{\sqrt{10 + 2\sqrt{5}}}{4}} + 3 \times \frac{1}{\frac{\sqrt{10 + 2\sqrt{5}}}{4}} - 4 \times \frac{\sqrt{10 + 2\sqrt{5}}}{4}$
$= 2 \times \frac{\sqrt{5} - 1}{\sqrt{10 + 2\sqrt{5}}} + 3 \times \frac{4}{\sqrt{10 + 2\sqrt{5}}} - \sqrt{10 + 2\sqrt{5}}$
$= \frac{2\sqrt{5} - 2 + 12 - \left( \sqrt{10 + 2\sqrt{5}} \right)^2}{\left( \sqrt{10 + 2\sqrt{5}} \right)}$
$= \frac{2\sqrt{5} + 10 - 10 - 2\sqrt{5}}{\left( \sqrt{10 + 2\sqrt{5}} \right)}$
$= 0$

Concept: Values of Trigonometric Functions at Multiples and Submultiples of an Angle
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 9 Values of Trigonometric function at multiples and submultiples of an angle
Q 6 | Page 43