[" (a) Prove that: "],[qquad log(1+e^(i theta))=log(2cos(theta)/(2))+(i theta)/(2)" if "-pi

The larger of cos(log theta) and log(cos theta) if (pi)/(2)

Find lim_(theta to 0)theta log(2-cos^2 theta)

Prove that: 2cos theta cos((pi)/(3)+theta)cos((pi)/(3)-theta)=cos3 theta

int cos2 theta log((cos theta+sin theta)/(cos theta-sin theta))=

Prove that : (cos(pi+theta)cos(-theta))/(sin (pi-theta) cos (pi/2+ theta))= cot^2 theta.

Prove that : (1-cos theta+i sin theta)/(1+i sin theta+cos theta)=ie^(-1)tan((theta)/(2))

The number of solutions of the equation (log_(2)cos theta)^(2)+log.(4)/(cos theta) (16 cos theta)=2 in the interval [0, 2pi) is

int cos 2theta log ((cos theta+sin theta)/(cos theta-sin theta))d theta

If: f(theta)=log((1+theta)/(1-theta)), then: f((2theta)/(1+theta^2))=

Which one is greater: cos(log_e theta)or log_e(costheta) if -pi/2ltthetaltpi/2