What is expand (-e^xsin(x)+cos(x)e^x)^2 ?

The solution to expand (-e^xsin(x)+cos(x)e^x)^2 is e^{2x}(-sin(2x)+1)

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expand (-e^xsin(x)+cos(x)e^x)^2

expand

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

e^{2 x} (- sin (2 x) + 1)

Solution steps

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

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

Apply Perfect Square Formula:

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

a = - e^{x} sin (x), b = cos (x) e^{x}

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

Simplify

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

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

Use the Double Angle identity:

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

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

Use the Pythagorean identity:

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

= e^{2 x} (- sin (2 x) + 1)

(y^{2} + 2^{y}) d y

(6 + 23) π

(x + 3 \circ x^{2}) \cdot 1

(2 x y) + (y^{2} - x^{2} - 4) y^{'} (x)

\frac{x - 1}{( x + 1 ) ( x - 2 )}

What is expand (-e^xsin(x)+cos(x)e^x)^2 ?
The solution to expand (-e^xsin(x)+cos(x)e^x)^2 is e^{2x}(-sin(2x)+1)