Q. $\cos{2\theta + 2\cos{\theta\ }}$is always
A) Greater than $- \frac{3}{2}$
B) Less than or equal to $\frac{3}{2}$
C) Greater than or equal to $- \frac{3}{2}$ and less than or equal to 3
D) None of the above
Explanation
(c)
$\cos{2\theta + 2\cos{\theta = 2\cos^{2}{\theta - 1 + 2\cos\theta}}}$
$= 2\left( \cos{\theta + \frac{1}{2}} \right)^{2} - \frac{3}{2} \geq - \frac{3}{2}\ \ \ \ \left\lbrack \because 2\left( \cos{\theta + \frac{1}{2}} \right)^{2} \geq 0,\forall\theta \right\rbrack$
Then maximum value of $\cos 2\theta + 2\cos{\theta\ is\ 3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.