If `log_(10)sin x + log_(10)cos x=-1` and `log_(10)(sin x + cos x)=((log_(10)n)-1)/(2)`, then the value of `'n//3'` is ......

Explanation

`log_10sinx+log_10cosx = -1`

`=>log_10 sinxcosx = -1`

`=>sinxcosx = 1/10`

Now, `sinx+cosx = sqrt((sinx+cosx)^2)`

`=sqrt(sin^2x+cos^2x+2sinxcosx)`

`=sqrt(1+2(1/10)`

`=sqrt(6/5)`

`:. sinx+cosx = sqrt(6/5)`

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