Question

Prove that `tantheta=(sintheta-2sin^3theta)/(2cos^3theta-costheta)`

Answer 1

We have
LHS `=(sin theta-2 sin^(3)theta)/(2cos^(3)theta-cos theta)=(sin theta(1-2sin^(2)theta))/(cos theta(2cos^(2) theta-1)) `
`=(sin theta(1-2sin^(2) theta))/(cos theta (2cos^(2)theta-1))`
` = tan theta*([1-2(1-cos^(2)theta)])/((2cos^(2) theta -1)) " " [ because sin^(2)theta=1- cos^(2)theta ] `
`= tan theta*((2cos^(2)theta-1))/((2cos^(2)theta-1))= tan theta = " RHS. " `
` therefore " LHS " = " RHS. " `