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prove $(\sin x+\cos x)^2=1+\sin 2x$

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Solve multi-step equations with fractional coefficients

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Q. prove

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

Expand Identity: Expand the left side using the identity $(a + b)^2 = a^2 + 2ab + b^2$ . $\newline$ $(\sin x + \cos x)^2 = \sin^2 x + 2\sin x \cos x + \cos^2 x$
Recognize Identity: Recognize that $\sin^2 x + \cos^2 x = 1$ . $\newline$ $\sin^2 x + \cos^2 x = 1$
Identify Double Angle Formula: Identify that $2\sin x \cos x$ is the double angle formula for $\sin 2x$ . $\newline$ $2\sin x \cos x = \sin 2x$
Substitute Identities: Substitute the identities into the expanded equation. $\newline$ $1 + 2\sin x \cos x = 1 + \sin 2x$
Check Equation: Check if the left side and the right side of the equation are the same. $\newline$ $1 + \sin 2x = 1 + \sin 2x$

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