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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: |
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Answer» 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]` |
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