Question

`sintheta/(1-cottheta)+costheta/(1-tantheta)=` (a)`theta` (b)1 (c)`costheta-sintheta` (d)`costheta+sintheta`

Answer 1

Correct Answer - D
`(sin theta)/(1-cot theta)+(cos theta)/(1-tan theta)`
`=(sin theta)/(1-(cos theta)/(sin theta))+(cos theta)/(1-(sin theta)/(cos theta))`
`=(sin^(2)theta)/(sin theta - cos theta)+(cos^(2)theta)/(cos theta - sin theta)`
`=(sin^(2)theta-cos^(2)theta)/((sin theta - cos theta))=sin theta + cos theta`