Show that `((1+cosphi+isinphi)/(1+cosphi-isinphi))^n=cosnphi+i sin nphi`

Using De Moivre 's theorem prove that : ((1+cos theta +i sin theta)/(1+cos theta - i sin theta))^n= cos n theta + i sin n theta , where i = sqrt(-1)

If a = cos theta + isin theta , b = cosphi + isinphi , c = cos psi + i sin psi and a/b+b/c+c/a=2 then sin(theta-phi)+sin(phi-psi)+sin(psi-theta) equals

If int(2sin2phi-cosphi)/(6-cos^(2)phi-4sinphi)dphi=p" ln "|sin^(2)phi-4sinphi+5|+qtan^(-1)(sinphi-r)+C then p+q+r equal to:

Show that, sqrt((1-"cos"A)/(1+"cos"A))=("sin"A)/(1+"cos"A)

If determinant |cos(theta+phi) sin(theta+phi)cos2phi sin thetacostheta sinphi costheta sintheta cosphi | is a. positive b. independent of theta c. independent of phi d. none of these

If tantheta=(xsinphi)/(1-xcosphi) and tanphi=(ysintheta)/(1-ycostheta), then x/y= (A) sinphi/sintheta (B) sintheta/sinphi (C) sinphi/(1-costheta) (D) sintheta/(1-cosphi)

Show that (1)/(2 sin 10^(@)) - 2 sin 70^(@) =1.

Evaluate the following indefinite integral: int(sinphi)/(sin^2phi+2cosphi+3)dphi

If theta+phi+psi=2pi, prove that cos^2theta+cos^2phi+cos^2psi -2costheta cosphi cospsi=1

Show that ((-1+sqrt(3)i)/2)^n+((-1-sqrt(3i))/2)^n is equal to 2 when n is a multiple of 3 and is equal to -1 when n is any other positive integer.