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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{1 - 2 e ^{- s} + e ^{- 2 s}}{s ( s ^{2} + 4 )}

(a^{2} b - 3)^{2}

\frac{1}{2} (5 + \frac{1}{2} ln (2 + 5))

\frac{1 + x}{1 - 2 x}

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