How do you simplify (4sinxcosx-2sinxsecx)/(2tanx)?

2 Answers
Sep 15, 2016

(4sinxcosx-2sinxsecx)/(2tanx)=cos2x

Explanation:

(4sinxcosx-2sinxsecx)/(2tanx)

= (4sinxcosx-2sinx/cosx)/(2sinx/cosx)

= (4sinxcosx)/(2sinx/cosx)-(2sinx/cosx)/(2sinx/cosx)

= (4sinxcos^2x)/(2sinx)-1

= 2cos^2x-1

= cos2x

Sep 15, 2016

LHS=(4sinxcosx-2sinxsecx)/(2tanx)

=(2sinx/cosx(2cos^2x-1))/(2tanx)

=(tanx(2cos^2x-1))/(tanx)

=(tanx(cos2x))/(tanx)=cos2x