1.

Solve sin^(2)theta-costheta=1/4 for theta and write the values of theta in the interval 0 lethetale2pi

Answer»

Solution :The GIVEN equation can be written as
`1-cos^(2)theta-costheta=1/4 rArr cos^(2)theta+costheta-3//4=0`
`rArr 4cos^(2)theta+4costheta-3=0 rArr (2costheta-1)(2costheta+3)=0`
`rArr costheta=1/2,-3/2`
Since, `costheta=-3//2` is not POSSIBLE as `-1 LE costhetale1`
`therefore costheta=1/2 rArr costheta=cospi/3 rArr theta=2npi+-pi/3, n in I`
For the given interval, n=0 and n=1
`rArr theta=pi/3, (5pi)/(3)`Ans.


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