Show that the equation 1+sinxtanx=5cosx can be expressed as 6cos^2-cosx-1=0?

1 Answer
Nov 12, 2017

See the proof below

Explanation:

We need

#tanx=sinx/cosx#

#sin^2x-cos^2x=1#

Therefore,

#1+sinxtanx=5cosx#

#1+sinx*sinx/cosx=5cosx#

Multiply by #cosx#

#cosx+sin^2x=5cos^2x#

Replacing #sin^2x# by #1-cos^2x#

#cosx+1-cos^2x=5cos^2x#

#5cos^2x-cos^2x-cosx-1=0#

#6cos^2x-cosx-1=0#

#QED#