if `sinB=1/2` then prove that `3cosB-4cos^3B=0`

If sin B= 1/2 find the value of 3 cosB- 4cos^3B .

If sinA/3=sinB/4=1/5 and A,B are angles in the second quadrant then prove that 4cosA+3cosB=-5

In any triangle ABC If sinA : sinB: sinC=4:5:6,then prove that cos A :cosB: cosC=12:9:2.

i) If sinA+sinB=sqrt(3)(cosB-cosA) , prove that: sin3A+sin3B=0 ii) If A,B and C are in arithmetic progression, then prove that: cotB=(sinA-sinc)/(cosC-cosA)

If sinA=sinB and cosA=cosB , then prove that sin((A-B)/2)=0

In sinA=sinB and cos A=cos B , then prove that sin(A-B)/(2)=0

In sinA=sinB and cos A=cos B , then prove that sin((A-B)/2)=0

If A+B+C=0^(@) then prove that sinA+sinB-sinC=-4"cos"A/2"cos"B/2"sin"C/2

If sinA=sinB and cosA=cosB , then prove that sin. (A-B)/(2)=0 .

If A+B+C = pi , prove that : cosA+cosB + cosC = 1+4sinA/2sinB/2sinC/2 .