How do you verify (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x?

2 Answers
Ho Kae Boon
May 1, 2018

Pretty sure the question is (sinx)(tanxcosx-cotxcos x)=1-2cos^2x ,or else it will be not provable.

Explanation:

Some basic knowledge to begin with:
1. sin^2x+cos^2x=1
2. tanx=sinx/cosx
3. cotx=cosx/sinx

Let's start from the left hand side
(sinx)(tanxcosx-cotxcos x)

=sinxtanxcosx-sinxcotxcosx

=sinx(sinx/cosx)cosx-sinx(cosx/sinx)cosx

=sin^2x-cos^2x

=sin^2x+cos^2x-2cos^2x

=1-2cos^2x

Jim G.
May 1, 2018

"see explanation"

Explanation:

"using the "color(blue)"trigonometric identities"

•color(white)(x)tanx=sinx/cosx" and "cotx=cosx/sinx

•color(white)(x)sin^2x+cos^2x=1

rArrsin^2x=1-cos^2x

"consider the left side"

"distributing the parenthesis"

sinx xxsinx/cancel(cosx)xxcancel(cosx)-cancel(sinx)xxcosx/cancel(sinx)xxcosx

=sin^2x-cos^2x

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

=1-2cos^2x=" right side "rArr"verified"

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