What is 2(sin(x)cos(x)-cos^2(x))+cos(2x)+sin(2x) ?

The solution to 2(sin(x)cos(x)-cos^2(x))+cos(2x)+sin(2x) is cos(2x)+2sin(2x)-2cos^2(x)

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simplify 2(sin(x)cos(x)-cos^2(x))+cos(2x)+sin(2x)

simplify

2 (sin (x) cos (x) - cos^{2} (x)) + cos (2 x) + sin (2 x)

cos (2 x) + 2 sin (2 x) - 2 cos^{2} (x)

Solution steps

2 (sin (x) cos (x) - cos^{2} (x)) + cos (2 x) + sin (2 x)

Expand

2 (sin (x) cos (x) - cos^{2} (x)) : 2 cos (x) sin (x) - 2 cos^{2} (x)

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

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

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

Add similar elements:

sin (2 x) + sin (2 x) = 2 sin (2 x)

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

e^{x^{x}} x^{x} (ln (x) + 1) + e^{x^{x}} x^{2 x} (ln (x) + 1)

(- sin (x)) (1 - sin (x))

\frac{1 - e ^{- x} + x ^{2} + 4 x}{x ( x ^{2} + 4 x + 5 )}

c (8, 4) yD I (12, - 4)

(i w + 1)^{2}

What is 2(sin(x)cos(x)-cos^2(x))+cos(2x)+sin(2x) ?
The solution to 2(sin(x)cos(x)-cos^2(x))+cos(2x)+sin(2x) is cos(2x)+2sin(2x)-2cos^2(x)