Question:medium

The value of \(\cos\frac{5\pi}{17}+\cos\frac{7\pi}{17}+2\cos\frac{11\pi}{17}\cos\frac{\pi}{17}\) is

Show Hint

Use \(2\cos A\cos B=\cos(A+B)+\cos(A-B)\), then apply \(\cos(\pi-\theta)=-\cos\theta\).

Updated On: May 7, 2026

\(0\)
\(1\)
\(-1\)
\(\frac{1}{2}\)

Show Solution

The Correct Option is A

Solution and Explanation

Was this answer helpful?

0

Top Questions on Trigonometry

If \( \tan^{-1}\left(\frac{1}{1+1\cdot2}\right) + \tan^{-1}\left(\frac{1}{1+2\cdot3}\right) + \ldots + \tan^{-1}\left(\frac{1}{1+n(n+1)}\right) = \tan^{-1}(x) \), then \( x \) is equal to:
- BITSAT - 2024
- Mathematics
- Trigonometry
View Solution
If \[ y = \tan^{-1} \left( \frac{1}{x^2 + x + 1} \right) + \tan^{-1} \left( \frac{1}{x^2 + 3x + 3} \right) + \tan^{-1} \left( \frac{1}{x^2 + 5x + 7} \right) + \cdots { (to n terms)} \], then \(\frac{dy}{dx}\) is:
- BITSAT - 2024
- Mathematics
- Trigonometry
View Solution
Let \(A\), \(B\) and \(C\) are the angles of a triangle and \(\tan \frac{A}{2} = 1/3\), \(\tan \frac{B}{2} = \frac{2}{3}\). Then, \(\tan \frac{C}{2}\) is equal to:
- BITSAT - 2024
- Mathematics
- Trigonometry
View Solution
The sum of all values of \(x\) in \([0, 2\pi]\), for which \(x + \sin(2x) + \sin(3x) + \sin(4x) = 0\) is equal to:
- BITSAT - 2024
- Mathematics
- Trigonometry
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in AP ECET Ceramic Tech exam

If \[ \frac{2x+5}{(x-1)(x+3)} = \frac{A}{x-1} + \frac{B}{x+3}, \] then \[ A+B = \; ? \]

AP ECET Ceramic Tech - 2025
Calculus

If \[ \frac{3x-1}{(x-1)(x-2)(x-3)} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{x-3}, \] then the values of \((A,B,C)\) are

AP ECET Ceramic Tech - 2025
Calculus

If \(\sin\theta=\frac{3}{5}\), then \(\cos\theta=\)

AP ECET Ceramic Tech - 2025
Trigonometry

If \(\cos\theta\cosec\theta=-1\) and \(\theta\) lies in the second quadrant, then \(\cos\theta=\)

AP ECET Ceramic Tech - 2025
Trigonometry