हल कीजिये `cot theta+3 tan theta=5" cosec" theta`

Explanation

`cot theta + 3 tan theta = 5 cosec theta " "` [दिया है]
`rArr " " (cos theta)/(sin theta)+3(sin theta)/(cos theta)=5 xx (1)/(sin theta)`
`rArr " " cos^(2)theta + 3 sin^(2) theta = 5 cos theta " " ` [`sin theta cos theta` से गुणा करने पर]
`rArr " " 3cos^(2)theta + 3 sin^(2)theta = 2 cos^(2)theta + 5 cos theta`
`rArr " " 3(cos^(2)theta + sin^(2)theta)=2 cos^(2)theta + 5 cos theta`
`rArr " " 3=2 cos^(2)theta + 5 cos theta`
`rArr " " 2 cos^(2)theta + 5 cos theta -3 = 0`
`rArr " " 2cos^(2)theta + 6 cos theta - cos theta - 3 =0`
`rArr 2 cos theta (cos theta + 3) -1 (cos theta + 3) = 0`
`rArr " " (cos theta + 3)(2 cos theta -1)=0`
यदि `" " cos theta + 3 = 0`
`rArr " " cos theta =-3, " "` जो असम्भव है |
और यदि `" " 2 cos theta - 1 =0`
`rArr " " cos theta =(1)/(2)"cos"(pi)/(3)`
`rArr " " theta = 2n pi pm (pi)/(3)`, जहाँ `n in I`.