If sinx+siny = a, cosx+cosy = b, prove that sin(x+y) = `(2ab)/(a^(2)+b^(2))`

If sinx + siny =a and cos x +cos y =b , show that sin(x+y) = 2ab/(a^(2)+b^(2)) and tan (x-y)/2 = sqrt((4-a^(2) -b^(2))/(a^(2) +b^(2))

If xcos theta- y sin theta =a, x sin theta + y cos theta = b , prove that: x^(2) + y^(2) = a^(2) + b^(2) .

If sinx/siny=1/2 and cosx/cosy=3/2 then sqrt(8+sec^2y)=

If sin x+siny=a, cosx+cosy=b , then what is the value of cos(x-y) ?

If x=a sin theta and y=b cos theta , then prove : (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

If x=a sin theta and y=b tan theta, then prove that (a^(2))/(x^(2))-(b^(2))/(y^(2))=1