Question:medium

\(1 + \cos x + \cos^2 x + \cos^3 x + \dots \text{ to } \infty = 4+2\sqrt{3}, \text{ then } x =\)

Show Hint

Always rationalize expressions like \( \frac{1}{A+\sqrt{B}} \) to see if they simplify into recognizable trigonometric values.

Updated On: Mar 26, 2026

\( n\pi \)
\( (4n \pm 1)\frac{\pi}{3} \)
\( (12n \pm 1)\frac{\pi}{6} \)
\( (3n \pm 1)\frac{\pi}{3} \)

Show Solution

The Correct Option is C

Solution and Explanation

Was this answer helpful?

0

Top Questions on Trigonometry

From the top of a 100 m high cliff, the angle of depression of a boat is $45^\circ$. Calculate the distance of the boat from the foot of the cliff.
- ICSE Class X board - 2026
- Mathematics
- Trigonometry
View Solution
A drone is flying at a height of 100 m above the ground. It observes on its right two stationary cars on a highway at angles of depression 45° and 30°. On the basis of above information, answer the following questions: If the drone rises to 150 m, find the tangent of the angle of depression of each car at the new height.
- UK Class X - 2026
- Mathematics
- Trigonometry
View Solution
A drone is flying at a height of 100 m above the ground. It observes on its right two stationary cars on a highway at angles of depression 45° and 30°. On the basis of above information, answer the following questions: Find the distance between the two cars.
- UK Class X - 2026
- Mathematics
- Trigonometry
View Solution
A drone is flying at a height of 100 m above the ground. It observes on its right two stationary cars on a highway at angles of depression 45° and 30°. On the basis of above information, answer the following questions: Find the distance of each car from the point on the highway just below the drone.
- UK Class X - 2026
- Mathematics
- Trigonometry
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in TS EAMCET exam

If $\omega \neq 1$ is a cube root of unity, then one root among the $7^{th}$ roots of $(1+\omega)$ is

TS EAMCET - 2025
Complex numbers

If $A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 1 & 1 \\ 1 & 3 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 3 & 4 \\ 3 & 2 & 2 \\ 2 & 4 & 2 \end{pmatrix}$, then $\sqrt{|\text{Adj}(AB)|} =$

TS EAMCET - 2025
Matrices and Determinants

If \( p_1, p_2, p_3 \) are the altitudes and \( a=4, b=5, c=6 \) are the sides of a triangle ABC, then \( \frac{1}{p_1^2} + \frac{1}{p_2^2} + \frac{1}{p_3^2} = \)

TS EAMCET - 2025
Geometry

If \(\alpha, \beta, \gamma, \delta, \epsilon\) are the roots of the equation \(x^5 + x^4 - 13x^3 - 13x^2 + 36x + 36 = 0\) and \(\alpha<\beta<\gamma<\delta<\epsilon\) then \( \frac{\epsilon}{\alpha} + \frac{\delta}{\beta} + \frac{1}{\gamma} = \)

TS EAMCET - 2025
Algebra