If sin x + cos x = t, then sin x cos x is equal to
t2−12
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 = sin2 x + cos2 x + 2 sin x cos x
t2= 1+ 2 sin x cos x
⇒ t2−12 = sin x cos x