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

By BYJU'S Exam Prep

Updated on: September 25th, 2023

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

Table of content

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:

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

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