Show that (sin ^2 X)/(1- cos X) = 1 + cos X Hence, solve (sin^2 X) / (1- cos - Maths - Trigonometry

Question

Show that (sin ^2 X)/(1- cos X) = 1 + cos X Hence, solve (sin^2 X)
/ (1- cos X) = cos 2X for 0° bigger than equal X lesser than
equal 360°

Neha Sethi · Accepted Answer

Consider sin2x1-cosx=1-cos2x1-cosx   sin2A+cos2A=1=1-cosx1+cosx1-cosx  A2-B2=A+BA-B=1+cosx=RHSConsider ,sin2x1-cosx=cos2x1+cosx=cos2x   As proved above⇒cos2x-cosx-1=0⇒2cos2x-1-cosx-1=0   using cos2A=2cos2A-1⇒2cos2x-cosx-2=0Using quadratic formula, we getcosx=--1±-12-42-222cosx=1±1+164cosx=1±172x=cos-11+172+2nπ  and x=cos-11-172 ,n∈Z

Show that (sin ^2 X)/(1- cos X) = 1 + cos X. Hence, solve (sin^2 X) / (1- cos X) = cos 2X for 0° bigger than equal X lesser than equal 360°