The number of integral values of `k` for which the equation `7cos x +5 sinx=2k+1` has a solution is (1) `4` (2) `8` (3) `10` (4) `12`

Explanation

`7cosx+5sinx=2k+1`

`7/sqrt(7^2+5^2)cosx+5/sqrt(7^2+5^2)sinx=(2k+1)/sqrt(7^2+5^2)`

`tanphi=7/5`

`sin(x+phi)=(2k+1)/sqrt74`

`-1<=sin(x+phi)<=1`

`=-1<=(2k+1)/sqrt74<-1`

after pitting the values.

4+4=8.

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