cot x -cot x cos^2 x
i know its prob really simple but i dont get it.
as much explanation as possible please as to how to get the answer. thanks
Im assuming the Q says : "Simplify". cotx-cotx(cos^2x)
cotx(1-cos^2x) [factorisation, cotx is common in both terms]
From the unit circle we know that sin^2x+cos^2x=1
so we can rearrange this like so: 1-cos^2x=sin^2x, now we can sub this in for the bracketed part
cotx(sin^2x)
now, cotx=cosx/sinx [Proof: cotx=adj/opp=(adj/hyp)/(opp/hyp)=cosx/sinx]
so we can write it as: cosx/sinx (sin^2x)
now one of those sinx cancel with the sinx on the denominator:
cosx(sinx) #
[If this is a 3U Q, the answer might be (1/2)sin2x, as sin2x=2sinxcosx] Otherwise the above line should be the answer you seek
