t^4 - 81

= (t^2)^2 - (3^2)^2

= (t^2 - 3^2)(t^2 + 3^2)

= (t - 3)(t + 3)(t^2 + 9)

cos(3t) = cos(2t + t) = cos(2t)*cos(t) - sin(2t)*sin(t)

= [cos2(t) - sin2(t)]*cos(t) - 2*cos(t)*sin(t)*sin(t)

= [cos2(t) - sin2(t)]*cos(t) - 2*cos(t)*sin2(t)

then, since sin2(t) = 1 - cos2(t)

= [2*cos2(t) - 1]*cos(t) - 2*cos(t)*[1 - cos2(t)]

= 2*cos3(t) - cos(t) - 2*cos(t) + 2*cos3(t)

= 4*cos3(t) - 3*cos(t)

Probability of T, T, T, T, T, T or 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 or 1/64 or 0.015625.

x2 is the same as x times x. In this case x = t+2 so we can say (t+2)2 is (t+2)(t+2) or t2+4t+4