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For what value of `k`the equation `sinx+cos(k+x)+cos(k-x)=2`has real solutions?

Answer» `sin x+cot (k+x)+cos (k-x)=2`
`rArr 2 cos x. cos k+sin x=2`
This equation is of the form `a cos x +b sin x=c`
Here `a=2 cos k, b=1` and `c=2`
Since for real solutions, `|c| le sqrt(a^(2)+b^(2))`, we have
`2 le sqrt(1+4 cos^(2) k)" "or" "cos^(2) k ge 3/4`
`rArr sin^(2) k le 1/4" "or" "sin^(2)k-1/4 le 0`
or `(sin k+1/2) (sin k-1/2) le 0`
or `-1/2 le sin k le 1/2`
`rArr (-pi)/6 le k le pi/6`


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