Question

If cos theta equal to 2p/1+P2 then find the value of tan theta

Answer 1

Answer:

LET N=125=Z^3

SINCE 125^1/3=5...WE CAN WRITE Z^3=(5^3)*1=(5^3){COS(2KPI)+iSIN(2KPI)}

SO Z =5*{COS(2KPI)+iSIN(2KPI)}^(1/3)

=5*{COS(2KPI/3)+iSIN(2KPI/3)}BY DEMOVIERS THEOREM...PUTTING K=1,2 AND 3 WE GET THE 3 CUBE ROOTS

5*{COS(2*1PI/3)+iSIN(2*1PI/3)}=5(-0.5+i*0.5*SQRT(3))=2.5(-1+i*SQRT(3))

5*{COS(2*2PI/3)+iSIN(2*2PI/3)}=5(-0.5-i*0.5SQRT(3))= -2.5(1+i*SQRT(3)

5*{COS2*3PI)+iSIN(2*3PI/3)}=5 .