If `sintheta=1/2 and sinphi=1/3`, find the value of `sin(theta+phi) and sin(2theta+2phi)`

If sin theta+ sin phi = a, cos theta + cos phi = b, find the value of sin ( theta+phi) and cos 2theta + cos 2phi where |b|>|a|

2sin(theta-phi)=sin(theta+phi)=1

If theta and phi are positive acute angles satisfying sin theta =1/2 and cos phi =1/3, then the value of (theta + phi) lies in the interval-

If sintheta+sinphi=2 ,then what is the value of cos(theta+phi)?

If sintheta+sinphi=a , costheta+cosphi=b find the value of tan((theta-phi)/2)

If tan theta = 1 and sin phi = (1)/( sqrt(2)) , then the value of cos (theta + phi) is

If sin theta+sin phi=a and cos theta+cos phi=b find the value of tan((theta-phi)/(2))

If theta+phi=(pi)/(2)andsintheta=(1)/(2) , then the value of sinphi is

IF tan^2 theta=2 tan^2 phi +1 then find the value of cos 2 theta+sin^2 phi .