The minimum value of cos 2theta + cos theta f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $S = \cos 2	heta + \cos 	heta$. Using the identity $\cos 2	heta = 2\cos^2 	heta - 1$,we get: $S = 2\cos^2 	heta - 1 + \cos 	heta$. Compl

Vedclass · Accepted Answer

$-9/8$

Vedclass · Answer

(A) Let $S = \cos 2	heta + \cos 	heta$. Using the identity $\cos 2	heta = 2\cos^2 	heta - 1$,we get: $S = 2\cos^2 	heta - 1 + \cos 	heta$. Completing the square for the expression in $\cos 	heta$: $S = 2(\cos^2 	heta + \frac{1}{2}\cos 	heta) - 1$. $S = 2(\cos^2 	heta + \frac{1}{2}\cos 	heta + \frac{1}{16} - \frac{1}{16}) - 1$. $S = 2(\cos 	heta + \frac{1}{4})^2 - \frac{1}{8} - 1$. $S = 2(\cos 	heta + \frac{1}{4})^2 - \frac{9}{8}$. Since the minimum value of $(\cos 	heta + \frac{1}{4})^2$ is $0$ (which occurs when $\cos 	heta = -1/4$,a valid value for $\cos 	heta$),the minimum value of $S$ is $-9/8$.

The minimum value of $\cos 2\theta + \cos \theta$ for real values of $\theta$ is

Similar Questions

If the equation $\cos^4 \theta + \sin^4 \theta + \lambda = 0$ has real solutions for $\theta$,then $\lambda$ lies in the interval

If $A + B + C = \frac{3\pi}{2},$ then $\cos 2A + \cos 2B + \cos 2C = $

If $f(x) = \sin^6 x + \cos^6 x$ for $x \in R$,then $f(x)$ lies in the interval

If $A + B = \frac{\pi}{2}$,what is the maximum value of $\cos A \cos B$?

If $A+B+C=180^{\circ}$,then the value of $\tan \left(\frac{A}{2}\right) \tan \left(\frac{B}{2}\right)+\tan \left(\frac{B}{2}\right) \tan \left(\frac{C}{2}\right)+\tan \left(\frac{C}{2}\right) \tan \left(\frac{A}{2}\right)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module