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

By Shivank Goel|Updated : August 3rd, 2022

Using the trigonometric identities, we can convert sin x + cos x into sine expression.

The question asked is - What is sin x + cos x in terms of sine?

With the help of Pythagorean identity

sin2x + cos2x = 1

cos2x = 1 - sin2x

Taking square root on both sides

cosx + sinx = sinx ± √1 - sin2x

By using the cofunction or complement identity

cosx = sin(π/2 - x)

sinx + cosx = sinx + sin(π/2 - x)

Therefore, when asked What is sin x + cos x in terms of sine? then the answer will be sin x + cos x in terms of sine is sinx + sin(π/2 - x).

Summary:

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

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

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