What is expand (cos(x)+sin(x))^3 ?

The solution to expand (cos(x)+sin(x))^3 is cos^3(x)+3cos^2(x)sin(x)+3sin^2(x)cos(x)+sin^3(x)

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expand (cos(x)+sin(x))^3

expand

(cos (x) + sin (x))^{3}

cos^{3} (x) + 3 cos^{2} (x) sin (x) + 3 sin^{2} (x) cos (x) + sin^{3} (x)

Solution steps

(cos (x) + sin (x))^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(cos (x) + sin (x))^{3} = cos^{3} (x) + 3 cos^{2} (x) sin (x) + 3 cos (x) sin^{2} (x) + sin^{3} (x)

= cos^{3} (x) + 3 cos^{2} (x) sin (x) + 3 cos (x) sin^{2} (x) + sin^{3} (x)

= cos^{3} (x) + 3 cos^{2} (x) sin (x) + 3 sin^{2} (x) cos (x) + sin^{3} (x)

(2 sin (x) + 1) (sin (x) - 1)

(3 x^{2} - 4 x + 1)^{5}

\frac{( 2 x + 3 ) ^{3}}{6}

(- 3 + i)^{7}

(2 cos (x) - 1)^{2}

What is expand (cos(x)+sin(x))^3 ?
The solution to expand (cos(x)+sin(x))^3 is cos^3(x)+3cos^2(x)sin(x)+3sin^2(x)cos(x)+sin^3(x)