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 $2$.

$$2 \sin^2a+3 \cos^2 a= 3\cos^2a+2-2\cos^2 a=\cos^2a+2$$
$$0\le \cos^2a \le 1 \Rightarrow 2\le \cos^2a+2 \le 3$$
