[" a) Prove that "],[qquad ((1+cos phi+i sin phi)/(1+cos phi-i sin phi))^(n)=cos n phi+i sin n phi*]

(3 cos phi+cos 3 phi)/(3 sin phi-sin 3 phi)=

Express the following in a + ib form: (a) ((cos alpha + i sin alpha)^(4))/((sin beta + i cos beta)^(5)) (b) ((1+ cos phi + i sin phi)/(1 + cos phi - isin phi))^(n) (c) ((cos alpha + i sin alpha)(cos beta + i sin beta))/((cos gamma + i sin gamma)(cos delta + i sin delta))

If ((1+cos phi+i sin phi)/(1+cos phi-i sin phi))^(n)=u+iv, where u and v all real numbers,then u is

Find int( (3 sin phi-2) cosphi)/(5-cos ^2 phi-4 sin phi) d phi

int((3sin phi-2)cos phi)/(5-cos phi-4sin phi)d phi

If a sin phi+b cos phi=c then a cos phi-b sin phi is

(1+sin phi+i cos phi)/((1+sin phi-i cos phi)^(n))=cos(n(pi)/(2)-n phi)+i sin(n(pi) /(2)-n phi)

Prove: (sin phi - cos phi) ^(2) =1 - sin 2 phi.