If `3cot(theta-pi/(12))=cot(theta+pi/12)`

3tan(theta - pi/12) = tan(theta + pi/12)

If x=sin(theta+(7 pi)/(12))+sin(theta+(pi)/(12))+sin(theta+(3 pi)/(12))Y=cos(theta+(7 pi)/(12))+cos(theta+(pi)/(12))+cos(theta+(3 pi)/(12)) then prove that (X)/(Y)-(Y)/(X)=2tan2 theta

Number of solutions of the equation cot( theta ) + cot( theta +(pi)/(3))+ cos ( theta -(pi)/(3))+ cot( 3 theta ) =0 , where theta in ( 0,(pi)/(2))

Number of solutions of the equation cot( theta ) + cot( theta +(pi)/(3))+ cos ( theta -(pi)/(3))+ cot( 3 theta ) =0 , where theta in ( 0,(pi)/(2))

Number of solutions of the equation cot( theta ) + cot( theta +(pi)/(3))+ cos ( theta -(pi)/(3))+ cot( 3 theta ) =0 , where theta in ( 0,(pi)/(2))

Number of solutions of the equation cot( theta ) + cot( theta +(pi)/(3))+ cos ( theta -(pi)/(3))+ cot( 3 theta ) =0 , where theta in ( 0,(pi)/(2))

If quad sin (theta + (7 pi) / (12)) + sin (theta- (pi) / (12)) + sin (theta + (3 pi) / (12)), Y = cos (theta + (7 pi) / (12)) + cos (theta- (pi) / (12)) + cos (theta + (3 pi) / (12)) then prove that (X) / (Y) - (Y) / (X) = 2tan2 theta

Prove that tan(theta+(pi)/(6))+cot(theta-(pi)/(6))=(1)/(sin2theta-sin.(pi)/(3))

The graph of cot theta , pi//2 lt theta lt 3 pi//2 is discontinuous at theta =