Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

If sum of all the solutions of the equation $8\cos x\cdot \left (\cos \left (\frac{\pi }{6} + x \right )\cdot\cos \left (\frac{\pi }{6}-x \right )- \frac{1}{2} \right ) = 1$ in $\left [ 0,\pi \right ]$ is $k\pi$
, then k is equal to :

Option 1)
$\frac{20}{9}$

Option 2)
$\frac{2}{3}$

Option 3)
$\frac{13}{9}$

Option 4)
$\frac{8}{9}$

Answers (2)

best_answer

$8\cos x \left ( \cos ^{2}\pi /6- \sin ^{2}x -1/2 \right )= 1$

$8\cos x \left ( -3/4- \cos ^{2}x )= 1$

$2(4\cos^{3}x- 3\cos x)= 1\Rightarrow \cos 3x= 1/2$

$3x= 2n\pi \pm \pi /3$

$n=0,n=1,n=2$

sum of all values = 13/9

Triple Angle Formula -

Triple angle formula

- wherein

These are formulae for triple angles.

General Solution of Trigonometric Ratios -

$\cos \Theta = \cos \alpha$

$\Theta = 2n\pi \pm \alpha , n\epsilon I$

- wherein

$\alpha$ is the given angle

Option 1)

$\frac{20}{9}$

Option 2)

$\frac{2}{3}$

Option 3)

$\frac{13}{9}$

Option 4)

$\frac{8}{9}$

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs

anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question