Join WhatsApp Icon JEE WhatsApp Group
Question 3

The number of values of $$a$$ for which the function $$f(x)=\cos 2x+2a(1+\cos x)$$ has a minimum value $$\frac{1}{2}$$ is

Solution

Share

Put $$t=\cos x$$, where $$-1\le t\le1$$. Then $$f(x)=2t^2+2at+2a-1$$. Checking the minimum of this quadratic on $$[-1,1]$$ shows that the required minimum $$\frac{1}{2}$$ occurs only for $$a=1$$, so there is exactly one such value.

Get AI Help

Other Cracku’s Useful Resources:

JEE Questions JEE Question Bank JEE Mains Previous Papers JEE Advanced Previous Papers JEE Study Material PDF JEE Mains Mock Test JEE Advanced Mock Test JEE Daily Target

Free JEE Questions

JEE Physics Questions JEE Maths Questions JEE Chemistry Questions
banner

50,000+ JEE Students Trusted Our Score Calculator

Predict your JEE Main percentile, rank & performance in seconds

Check Your Score Now
Ask AI