Simplify the following expressions to single trigonometric f

Simplify the following expressions to single trigonometric functions. cos (tan -sec ) 1-csc 20. Ans:

Solution

20) cos theta ( tan theta - sec theta ) / ( 1 - csc theta )

tan theta = sin theta / cos theta

sec theta = 1 / cos theta

csc theta = 1 / sin theta

cos theta ( sin theta / cos theta - 1 / cos theta ) / ( 1 - 1 / sin theta )

cos theta ( sin theta -1 ) / cos theta / ( 1 - 1/ sin theta )

( sin theta -1 ) / ( sin theta - 1 ) / sin theta

simplified form is

= sin theta