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).
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