If `X=sin(theta+(7pi)/12)+sin(theta-pi/12)+sin(theta+(3pi)/12), Y=cos(theta+(7pi)/12)+cos(theta-pi/12)+cos(theta+(3pi)/12)` then prove that `X/Y-Y/X=2tan2theta`

If x=sin(theta+(7pi)/(12))+sin(theta-pi/(12))+sin(theta+(3pi)/(12))dot Y=cos(theta+(7pi)/(12))+cos(theta-pi/(12))+cos(theta+(3pi)/(12))dot then prove that X/Y-Y/X=2tan2theta

If x=sin(theta+(7pi)/(12))+sin(theta+pi/(12))+sin(theta+(3pi)/(12))dot Y=cos(theta+(7pi)/(12))+cos(theta+pi/(12))+cos(theta+(3pi)/(12))dot then prove that X/Y-Y/X=2tan2theta

If x=sin(theta+(7pi)/(12))+sin(theta+pi/(12))+sin(theta+(3pi)/(12))dot Y=cos(theta+(7pi)/(12))+cos(theta+pi/(12))+cos(theta+(3pi)/(12))dot then prove that X/Y-Y/X=2tan2theta

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

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

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

If tan((pi)/(2) sin theta)=cot((pi)/(2)cos theta) then sin(theta +(pi)/(4))=

int_(pi//4) ^(pi//2) (cos theta)/((cos (theta/2) + sin (theta/2))^(3))d theta=

If tan((pi)/(2) sin theta )= cot((pi)/(2) cos theta ) , then sin theta + cos theta is equal to