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

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

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

expand

(5 cos (π x) + sin (5 π x))^{2}

25 cos^{2} (π x) + 10 cos (π x) sin (5 π x) + sin^{2} (5 π x)

Solution steps

(5 cos (π x) + sin (5 π x))^{2}

Apply Perfect Square Formula:

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

a = 5 cos (π x), b = sin (5 π x)

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

Simplify

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

= 25 cos^{2} (π x) + 10 cos (π x) sin (5 π x) + sin^{2} (5 π x)

y (2 x y^{'} (x) - y)

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

2 \cdot (3 x + 16) - 8 = 20

\frac{5 ( x + 1 )}{( x + 7 )}

\frac{( x + h ) ^{2} - 5}{h}

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