Maximum minimum values in trigonometry 
Find minimum value of $2\sin^2a+3\cos^2a$

Solving it we get $2+ \cos^2a$

Answer: $3$ (taking $\cos a$ as $-1$)

Why are we using the minimum cosine value as $-1$ instead of using the cosine as $0$? 
This can make the minimum value as $2$.

Differentiate the function to get $-2cos\alpha sin\alpha$ and set it to $0$. This gives $sin2\alpha=0$ or $\alpha=0$.
