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Solve `2sin^(2)x-5sinxcosx-8cos^2x=-2`

Answer» `2sin^2x-5sinxcosx-8cos^2x = -2`
Dividing this equation by `cos^2x`,
`=>2tan^2x - 5tanx - 8 = -2sec^2x`
`=>2tan^2x - 5tanx - 8 = -2(1+tan^2x)`
`=>2tan^2x - 5tanx - 8 = -2-2tan^2x)`
`=>4tan^2x - 5tanx - 6 = 0`
`=>4tan^2x - 8tanx +3tanx - 6 = -0`
`=>(4tanx+3)(tanx-2) = 0`
`=>tanx = -3/4 and tanx = 2`
`=> x = npi+tan^-1(-3/4) and x = npi+tan^-1(2).`


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