The general values of theta satisfying t...

The general values of `theta` satisfying the equation `2sin^2thetapi-3sinthetapi-2=0` is `(n in Z)dot` `npi+(-1)^npi/6` (b) `npi+(-1)^npi/2` `npi+(-1)^n(5pi)/6` (d) `npi+(-1)^n(7pi)/6`

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`(sinx+sin3x) - 3sin2x = (cosx+cos3x) - 3cos2x`
`=>(2sin2xcosx) - 3sin2x = (2cos2xcosx) - 3cos2x`
`=>sin2x(2cosx-3) = cosx(2cosx-3)`
`=>sin2x = cos2x`
`=>tan2x = 1`
`=>2x = npi+pi/4`
`=>x = (npi)/2+pi/8`
So, option - `(b)` is the correct option.

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