Question

If sin x + cos x = t, then sin x cos x is equal to

• A. $\frac{t^2-1}{2}$
• B. $\frac{t^2+1}{2}$
• C. $\sqrt{2-t^2}$
• D. $\sqrt{t^2-1}$

Answer 1

The correct option is A

$\frac{t^2-1}{2}$

We want to get sin x cos x from sin x + cos x. if we square sin x + cos x, one of the terms will be 2 sin x cos x. so we will consider $(sinx+cosx{)}^2$.
⇒ $(sinx+cosx{)}^2$ = $si{n}^2$ x + $co{s}^2$ x + 2 sin x cos x

$t^2$= 1+ 2 sin x cos x
⇒ $\frac{t^2-1}{2}$ = sin x cos x