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

Solution:

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

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).

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

Summary:

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