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

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

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simplify (cos(2pit+2pit))^2

simplify

(cos (2 π t + 2 π t))^{2}

cos^{2} (4 π t)

Solution steps

cos^{2} (2 π t + 2 π t)

Rewrite using trig identities

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

Use the Double Angle identity:

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

= cos^{2} (2 \cdot 2 π t)

Multiply the numbers:

2 \cdot 2 = 4

= cos^{2} (4 π t)

sin (arccos (x - 1))

4 sin (2 x - \frac{π}{4}) + 1

tan (arccos (w))

cos (- n \cdot π)

sec (x - \frac{2 π}{3})