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

The solution to expand (sin(x)+(cos(x))^2)^2 is sin^2(x)+2cos^2(x)sin(x)+cos^4(x)

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expand (sin(x)+(cos(x))^2)^2

expand

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

sin^{2} (x) + 2 cos^{2} (x) sin (x) + cos^{4} (x)

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

sin^{2} (x) + 2 sin (x) cos^{2} (x) + (cos^{2} (x))^{2} : sin^{2} (x) + 2 cos^{2} (x) sin (x) + cos^{4} (x)

= sin^{2} (x) + 2 cos^{2} (x) sin (x) + cos^{4} (x)

(20 (- 1 + \frac{k}{n})^{3} + 20 (- 1 + \frac{k}{n})^{2}) \cdot \frac{1}{n}

- \frac{1}{4} (x - 34)^{2} (x - 41) + 45

\frac{1}{( s + 3 ) ( s ^{2} - 5 s + 10 )}

\frac{d y}{y} (- 3, - 5) (0, 10)^{''}

\frac{1}{5} (3 ln \frac{x ^{2}}{4} + 1 + 2 arctan (\frac{x}{2}))

What is expand (sin(x)+(cos(x))^2)^2 ?
The solution to expand (sin(x)+(cos(x))^2)^2 is sin^2(x)+2cos^2(x)sin(x)+cos^4(x)