Solve for x and y :12.sinx -2.(y)^2 = 21 - 8.y - 5.cosx

Given 12sinx-2y^2=21-8y-5cosxRearrange the above equation2y^2-8y-12sinx+21-5cosx=0It`s the quadratic equation in y therefore ∆>=0(8)^2>=4×2(-12sinx-5cosx+21)8^2>=8×[-12sinx-5cosx+21]min value of -12sinx-5cosx=13Substitute in above equationSo 64>=8×[21-13]64>=8×864>=6464=64Therefore 12sinx+5cosx=13Therefore sinx=12/13 And cosx=5/13

Approved