Remember:
color(red)("Basic definitions:")Basic definitions:
color(white)("XXX")color(red)(tan(theta)=sin(theta)/cos(theta)color(white)("XXX")cot(theta)=cos(theta)/sin(theta))XXXtan(θ)=sin(θ)cos(θ)XXXcot(θ)=cos(θ)sin(θ)
color(blue)("Double angle formulae for sin and cos")Double angle formulae for sin and cos
color(white)("XX"color(blue)(sin(2theta)=2 * sin(theta) * cos(theta)color(white)("XX")cos(2theta)=cos^2(theta)-sin^2(theta))XXsin(2θ)=2⋅sin(θ)⋅cos(θ)XXcos(2θ)=cos2(θ)−sin2(θ)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Required to Prove:
color(green)(cot(x)-tan(x)=2cot(2x)cot(x)−tan(x)=2cot(2x)
Proof:
R.S.R.S.
color(white)("XXX")=color(green)(2cot(2x))XXX=2cot(2x)
color(white)("XXX")=2 * cos(2x)/sin(2x)XXX=2⋅cos(2x)sin(2x)
color(white)("XXX")=(cancel2 * (cos^2(x)-sin^2(x)))/(cancel2 * sin(x) * cos(x))
color(white)("XXX")=cos^2(x)/(sin(x) * cos(x)) - sin^2(x)/(sin(x) * cos(x))
color(white)("XXX")=cos(x)/sin(x) -sin(x)/cos(x)
color(white)("XXX")=color(green)(cot(x)-tan(x))
color(white)("XXX")=L.S.
