if `a = costheta +i sin theta `, prove that `(1+a)/(1-a) = cot(theta/2)i`

If a=cos theta+i sin theta, then (1+a)/(1-a) is equal to ( i) cot((theta)/(2))( ii) cot theta( iii) i cot((theta)/(2))( iv )i tan((theta)/(2))

If a=cos theta+i sin theta, then (1+a)/(1-a)=(cot theta)/(2) b.cot theta c.i(cot theta)/(2)d*i(tan theta)/(2)

If alpha=cos theta+i sin theta, then (1+alpha)/(1-alpha) equals ( (i)cot theta(ii)i tan((theta)/(2))(iii)i cot((theta)/(2))(iv)cot((theta)/(2))

Prove that (1+cos theta)/(sin theta)=cot[(theta)/(2)]

Prove that sin(2theta)/(1-cos2theta)=cot theta

Prove that: (sin2 theta)/(1-cos2 theta)=cot theta

Prove that (cot theta + "cosec" theta -1 )/(cot theta - "cosec" theta +1)=(1+ cos theta)/(sin theta).

Prove that (cot theta + "cosec" theta -1 )/(cot theta - "cosec" theta +1)=(1+ cos theta)/(sin theta).

If sin^2theta + sin^ 4theta = 1 , then prove that cos^2theta+ costheta= 1

prove that 1/(cosec theta-cot theta) - 1/(sin theta) = 1/sin theta - (1)/(cosec theta + cot theta)