Key to "²(sin⁡x+cos⁡x)²=1+sin⁡2x"

Ayaana Buck

Answered question

2021-06-05

(\sin x + \cos x) ² = 1 + \sin 2 x

pivonie8

Skilled2021-06-06Added 91 answers

Work on the left side. Expand using the rule:

{(a + b)}^{2} = a^{2} + 2 a b + b^{2}

{(\sin x + \cos x)}^{2} = (\sin^{2}) x + 2 \sin x \cos x + (\cos^{2}) x

Use the identity:

(\sin^{2}) x + (\cos^{2}) x = 1

{(\sin x + \cos x)}^{2} = (\sin^{2}) x + (\cos^{2}) x + 2 \sin x \cos x

{(\sin x + \cos x)}^{2} = 1 + 2 \sin x \cos x

Use the double angle identity:

\sin 2 x = 2 \sin x \cos x

{(\sin x + \cos x)}^{2} = 1 + \sin 2 x

Jeffrey Jordon

Expert2021-09-14Added 2605 answers

Answer is given below (on video)

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