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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{d}{d x} ((x^{2} + 1) arctan (x)) - x

(\frac{5}{2} x + \frac{3}{4} y)^{2}

f a cot (r) (- 16 x^{3} + 33 x^{2} - 18 x + 1)

144 x^{5} - 3 x (3 + 16 x^{\frac{9}{2}})

(2.1) (3 x - 4 y + 10 = 0)

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