FIND COS THETA/2, SIN THETA/2,TAN THETA/2

Question

KINDLY SHOW ME THE STEP BY STEP SOLUTION. I NID IT AS A SAMPLE FOR R UPCOMING EXAM. TY IN ADVANS!!!

Answer 1

cos(theta)=cos(2*(theta/2))=2cos^2(theta/2)-1=cos^2(theta/2)-sin^2(theta/2)=1-2sin^2(theta/2).

From these: 2cos^2(theta/2)=1+cos(theta); cos^2(theta/2)=(1+cos(theta))/2; cos(theta/2)=sqrt((1+cos(theta))/2);

sin^2(theta/2)=(1-cos(theta))/2;

sin(theta)=sqrt((1-cos(theta))/2).

sin(theta/2)/cos(theta/2)=

tan(theta/2)=sqrt((1-cos(theta))/(1+cos(theta)))=

sqrt((1-cos^2(theta))/(1+cos(theta))^2)=

sqrt(sin^2(theta)/(1+cos(theta))^2)=sin(theta)/(1+cos(theta)).