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If (log)(10)sinx+(log)(10)cosx=-1a n d(l...

If `(log)_(10)sinx+(log)_(10)cosx=-1a n d(log)_(10)(sinx+cosx)=(((log)_(10)n)-1)/2,` then the value of `' n//3'` is_______

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`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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