1.

Prove that `( sin 5x - 2 sin 3x + sin x )/( cos 5x - cos x) = tan x`

Answer» Here, we will use the following rules,
`sinA - sinB = 2cos((A+B)/2)sin((A-B)/2)`
`cosA-cosB = -2sin((A+B)/2)sin((A-B)/2)`
`L.H.S. = (sin5x - 2sin3x+sinx)/(cos5x-cosx)`
`= ((sin5x - sin3x)-(sin3x-sinx))/(cos5x-cosx)`
`=(2cos4xsinx - 2cos2xsinx)/(-2sin3xsin2x)`
`=(sinx(cos4x-cos2x))/(-sin3xsin2x)`
`=(sinx(-2sin3xsinx))/(-sin3xsin2x)`
`=(2sin^2x)/(sin2x)`
`= (2sin^2x)/(2sinxcosx)`
`=sin/cosx = tanx = R.H.S.`


Discussion

No Comment Found

Related InterviewSolutions