Homework SourseForm an identity by completing the following equation sin x
Form an identity by completing the following equation. (sin x - cos x)^2 + (sin x + cos x )^2= 2] 2(sin x - cos x)^2 (sin2x - cos2x) None of the above.![Form an identity by completing the following equation. (sin x - cos x)^2 + (sin x + cos x )^2= 2] 2(sin x - cos x)^2 (sin2x - cos2x) None of the above.Solution](/WebImages/24/form-an-identity-by-completing-the-following-equation-sin-x-1059020-1761552938-0.webp "Form an identity by completing the following equation. (sin x - cos x)^2 + (sin x + cos x )^2= 2] 2(sin x - cos x)^2 (sin2x - cos2x) None of the above.Solution")
Solution
(sinx - cosx)^2 + (sinx +cosx)^2
use the formula : ( a + /- b)^2 = a^2 +b^2 +/- 2ab
So,(sinx - cosx)^2 = sin^2x +cos^2x- 2sinxcosx = 1-2sinxcosx = 1 - sin2x
(sinx +cosx)^2 = sin^2x +cos^2x+ 2sinxcosx = 1 + 2sinxcosx = 1 + sin2x
(sinx - cosx)^2 + (sinx +cosx)^2 = 1 - sin2x + 1 + sin2x = 2
Option A
