What is sin x + cos x in terms of sine?

To convert sin x + cos x into sine expression we will be making use of trigonometric identities.

Answer : The expression for sin x + cos x in terms of sine is sin x + sin (π / 2 – x).

Let us see the detailed solution now.

Explanation:

Using pythagorean identity,

Sin²x +Cos²x = 1

So, Cos²x = 1 - Sin²x

By taking square root on both the sides,

Cosx + Sinx = Sinx ±√1 − Sin²x

Using complement or cofunction identity,

Cosx = Sin(π/2−x)

Sinx + Cosx = Sinx + Sin(π/2−x)

Thus, the expression for sin x + cos x in terms of sine is sin x + sin ( π/2 – x).