Find the gereral of the equation `sinx-3sin2x+sin3x=cosx-3cos2x+cos3x`.

Options

A. `x=(npi)/(2)+(pi)/(2)`
B. `x=(npi)/(2)+(pi)/(4)`
C. `x=(npi)/(2)+(pi)/(6)`
D. `x=(npi)/(2)+(pi)/(8)`

Answer

D

Explanation

Given equation, `sinx-3sin2x+sin3x=cosx-3cos2x+cos3x`
`rArr" "2sin((x+3x)/(2))*cos((3x-x)/(2))-3sin2x`
`" "=2cos((3x+x)/(2))*cos((3x-x)/(2))-3cos2x`
` rArr" "2sin2xcosx-3sin2x=2cos2x*cosx-3cos2x`
` rArr" "sin2x(2cosx-3)=cos2x(2cosx-3)`
`rArr" "(sin2x)/(cos2x)=1`
`rArr" "tan2x=tan""(pi)/(4)`
`rArr" "2x =npi+(pi)/(4)`
`therefore" "x=(npi)/(2)+(pi)/(8)`