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Find the general value of theta from the...

Find the general value of `theta` from the equation `sinptheta=cosqtheta`.

Text Solution

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`sinptheta=cosqtheta`
`rArr cosqtheta=sinptheta`
`=cos(pi/2-ptheta)`
`rArr qtheta=2npi+-(pi/2-ptheta)`
`rArr (p+q)theta=2npi+pi/2=(4n+1)pi/2`
`rArr theta=((4n+1)pi)/(2(p+q))`. Ans.
`qtheta=2npi-(pi/2-ptheta)`
`rArr (q-p)theta=2npi-pi/2=(2n-1)pi/2`
`rArr theta=((4n-1)pi)/(2(q-p))`. Ans.
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