1.

If sin^(4)x + cos^(4)y + 2 = 4 sinx cosy and 0 le x, y le pi/2. Then sinx + cos y is equal to:

Answer»

`-2`
0
`3/2`
2

Solution :`sin^(4)x + cos^(4)y +2 = 4 sinx cosy`
`(sin^(2)x-1)^(2) + (cos^(2)y-1)^(2) + 2 sin^(2)x + 2 cos^(2)y - 4 sinx cosy =0`
`(sin^(2)x -1)^(2) + (cos^(2)y-1)^(2)+ 2(sinx - cosy)^(2)=0`
Which is TRUE if
`(sin^(2)x -1)^(2) +(cos^(2)y -1)^(2) + 2(sin x- cosy)^(2)=0`
Which is true is
`sin^(2)x =1, cos^(2)y, sin^(2)x = cos^(2)y`
`RARR sinx = cosy=1 therefore x,y in [0, pi/2]`


Discussion

No Comment Found

Related InterviewSolutions