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Solve (3 sin theta-sin 3 theta)/(sin the...

Solve `(3 sin theta-sin 3 theta)/(sin theta)+(cos 3 theta)/(cos theta)=1`.

Text Solution

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We have
`(3 sin theta- sin 3 theta)/(sin theta)+(cos 3 theta)/(cos theta)=1`
`:. (4 sin^(3) theta)/(sin theta)+((4 cos^(3) theta-3 cos theta))/(cos theta)=1`
`rArr 4 sin^(2) theta+4 cos^(2) theta -3 =1`
`rArr 1=1`
This is always true except `theta= (npi)/2, n in Z` for which either `sin theta` or `cos theta` is zero.
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