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

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

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

expand

(sin (π t) + cos^{2} (π t))^{2}

sin^{2} (π t) + 2 cos^{2} (π t) sin (π t) + cos^{4} (π t)

Solution steps

(sin (π t) + cos^{2} (π t))^{2}

Apply Perfect Square Formula:

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

a = sin (π t), b = cos^{2} (π t)

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

(cos^{2} (π t))^{2} = cos^{4} (π t)

= sin^{2} (π t) + 2 cos^{2} (π t) sin (π t) + cos^{4} (π t)

\frac{1}{2} (3 + 4 sin (2 x) - cos (4 x))

ln (x + 1) (x + 1)

(x^{2} - (\frac{1}{x})^{4})^{2}

(3 - 1)^{5}

sin (α) (1 + tan (α)) + cos (α) (1 + cot (α))

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