Question

if cos θ+root 3 sinθequals 2sinθshow that sin theta -root 3cos theta equals2 cos theta

Answer 1

cosA+√3sinA=2sinA
cosA = 2sinA -√3sinA
cosA=sinA (2-√3)
sinA/cosA = 2-√3 i.e cotA = 2-√3 --(1)
sinA -√3cosA =2cosA
sinA = 2cosA +√3 cosA
sinA = cosA (2+√3 )
sinA /cosA=2+√3 i.e tanA =2+√3 --(2)
we know that tanA×cotA =1
(2-√3 )(2+√3 )=2^2 -√3 ^2
=2-3 = 1
therefore both equations are equal
sinA - √3 cosA = 2cosA