solve for cosec x- cosec 2x = cosec4x Share with your friends Share 7 Vijay Kumar Gupta answered this Consider the following equation. cosecx-cosec2x=cosec4xUse the reciprocal identity, cosecx=1sinx to get, 1sinx-1sin2x=1sin4x 1sinx=1sin2x+1sin4x 1sinx=sin4x+sin2xsin2x sin4x sin2x sin4xsinx=sin4x+sin2xUse the trigonometric identities. sin2x=2sinx cosx sinx+siny=2 sinx+y2cosx-y2This implies that, 2sinx cosx sin4xsinx=2 sin4x+2x2cos4x-2x2 2cosx sin4x=2 sin3x cosxCancel the common factors on both sides to get, sin4x=sin3xNow sinx=siny implies that x=nπ+-1ny, n∈ZThis gives, 4x=nπ+-1n3x, n∈Z 4x--1n3x=nπ, n∈Z 4x+-1-1n3x=nπ, n∈Z 4x+3-1n+1x=nπ, n∈Z 4+3-1n+1x=nπ, n∈ZTherefore the required solution is, x=nπ4+3-1n+1, n∈Z -9 View Full Answer
