If `5sec theta-12 cosec theta=0`, find the values of `sec theta, cos theta` and `sin theta`.

Explanation

`5 sec theta - 12 cosec theta = 0`.
`therefore 5 sec theta = 12 cosec theta`
`therefore (sec theta)/(cosec theta) = (12)/(5)`
`therefore sec theta div cosec theta = (12)/(5)`
`therefore (1)/(cos theta) div (1)/(sintheta) = (12)/(5)`
.....`[sec theta = (1)/(cos theta), cosec theta = (1)/(sin theta) ]`
`therefore (1)/(cos theta)xx(sin theta)/(1) = (12)/5`
`therefore (sintheta)/(costheta) = (12)/5` ....(1)
`therefore tan theta = (12)/5` .....(2)
`1 + tan^2 theta = sec^2theta`
`therefore sec^2theta 1 + ((12)/(5))^2 = sec^2theta`
`therefore sec^2theta = 1+(144)/(25)`
`therefore sec^2 theta = (25 + 144)/(25)`
`therefore sec^2theta = (169)/(25)`
`therefore sectheta = (13)/5` ...(3)
... (Taking square roots of both the sides )
`cos theta = 1/(sec theta)" " therefore theta = 1/(((13)/(5)))`
`therefore cos theta = 5/(13)` ...(4)
`(sin theta)/(cos theta)= (12)/5` ...[From (1)]
` therefore sin theta = (12)/5xxcos theta`
` =(12)/5xx(5)/(13)` ...[From(4) ]
`therefore sin theta = (12)/(13)`
`sec theta, cos theta 5/(13) and sin theta = (12)/(13)`.