What is expand (sin(x)+5cos(x))^2 ?

The solution to expand (sin(x)+5cos(x))^2 is sin^2(x)+10cos(x)sin(x)+25cos^2(x)

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expand (sin(x)+5cos(x))^2

expand

(sin (x) + 5 cos (x))^{2}

sin^{2} (x) + 10 cos (x) sin (x) + 25 cos^{2} (x)

Solution steps

(sin (x) + 5 cos (x))^{2}

Apply Perfect Square Formula:

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

(sin (x) + 5 cos (x))^{2} = sin^{2} (x) + 2 sin (x) \cdot 5 cos (x) + (5 cos (x))^{2}

= sin^{2} (x) + 2 sin (x) \cdot 5 cos (x) + (5 cos (x))^{2}

Simplify

sin^{2} (x) + 2 sin (x) \cdot 5 cos (x) + (5 cos (x))^{2} : sin^{2} (x) + 10 cos (x) sin (x) + 25 cos^{2} (x)

= sin^{2} (x) + 10 cos (x) sin (x) + 25 cos^{2} (x)

\frac{( 2 - 3 x ^{2} ) ^{5}}{5 x}

(1 + 4 sin (t)) (4 cos (t))

(x_{0} + α x_{1})^{3}

(e^{- x^{2}} - 2 e^{- x^{2}} x^{2})^{2}

(f \circ g) (2 x^{2} + x)

What is expand (sin(x)+5cos(x))^2 ?
The solution to expand (sin(x)+5cos(x))^2 is sin^2(x)+10cos(x)sin(x)+25cos^2(x)