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

The solution to expand (cos(x)+3sin(x))^2 is cos^2(x)+6cos(x)sin(x)+9sin^2(x)

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expand (cos(x)+3sin(x))^2

expand

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

cos^{2} (x) + 6 cos (x) sin (x) + 9 sin^{2} (x)

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

cos^{2} (x) + 2 cos (x) \cdot 3 sin (x) + (3 sin (x))^{2} : cos^{2} (x) + 6 cos (x) sin (x) + 9 sin^{2} (x)

= cos^{2} (x) + 6 cos (x) sin (x) + 9 sin^{2} (x)

(sin (2 x))^{2}

\frac{x ^{3}}{( x - 2 ) ( x + 1 )}

(tan (x) - sin (x))^{2} + (1 - cos (x))^{2}

sin (0)

3 cos (π (x - 1))

What is expand (cos(x)+3sin(x))^2 ?
The solution to expand (cos(x)+3sin(x))^2 is cos^2(x)+6cos(x)sin(x)+9sin^2(x)