1.

Solve `sin 2 theta+cos theta=0`.

Answer» We have `sin 2 theta+cos theta=0`
or `cos theta=- sin 2 theta = cos (pi/2+2 theta)`
`rArr theta=2 n pi pm (pi/2+2 theta) n in Z`
Taking positive sign, we have
`theta=2 npi + pi/2 +2 theta`
`theta=2 n pi - pi/2, n in Z`
Taking negative sign, we have
`theta=2 n pi -(pi/2+2 theta)`
`rArr theta=(2 n pi)/3-pi/6, n in Z`


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