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

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

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

expand

(5 cos (π t) + sin (5 π t))^{2}

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

Solution steps

(5 cos (π t) + sin (5 π t))^{2}

Apply Perfect Square Formula:

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

a = 5 cos (π t), b = sin (5 π t)

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

Simplify

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

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

sin (2) (π + x)

\frac{( x + 6 ) ( x - 8 )}{( x + 8 ) ( x + 7 )}

\frac{1}{s ^{3} ( s - 2 ) ^{2}}

\frac{2 ( L s ^{2} C + 1 )}{3 s C}

\frac{6}{( x - 4 ) ^{3}}

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