If `2cosx+sinx=1,` then find the valie of `7x+6sinxdot`

Explanation

Given, `2cosx+sinx=1 …(i)`
or `4cos^2x=(1-sinx)^2`
`or 4-4sin^2x=1+sin^2x-2sinx`
or `5sin^2x-2sinx-3=0`
or `(sinx-1)(5sin+3)=0`
or `sinx=1,sinx=-3/5`
for `sinx=1,` we have
`7cosx+6sinx=0+6=6`
and for `sinx=(-3)/5`,we have
`7cosx+6sinx=7((1+3/5)/2)-(6xx3)/5`
`=(28-18)/5=2`