tmua.me Extreme Set A Paper 2 · Question 13

Let $a$ and $b$ be real constants. Consider the condition

a^2\leq4b

and the following statement:

For every real angle $\theta$ , if

\sin^2\theta+a\sin\theta\cos\theta+b\cos^2\theta=0,

then $\sin^2\theta=\cos^2\theta$ .

Which of the following correctly describes the condition in relation to the statement?

AThe condition is necessary but not sufficient.

BThe condition is sufficient but not necessary.

CThe condition is both necessary and sufficient.

DThe condition is neither necessary nor sufficient.

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