Simplify completely: 1/cot2x - 1/cos2x. Select your answer from the choices below

Question

Simplify completely: 1/cot2x - 1/cos2x. Select your answer from the choices below

1

-1

Sec x

Tan x

Answer 1

1/cot2x - 1/cos2x

=sin(2x)/cos(2x)-1/cos(2x)

=(sin(2x)-1)/cos(2x)
=-(cos²x-2sinxcosx+sin²x)/(cos²x-sin²(x))
=-(cosx-sinx)²/[(cosx-sinx)(cosx+sinx)]
=(sinx-cosx)/(sinx+cosx)=(tan(x)-1)/(tan(x)+1)

=(tan(x)-tan(π/4))/(tan(x)+1)

=tan(x-π/4)(1+tan(x))/(1+tan(x))=tan(x-π/4).

 

Answer 2

1/cot2x- 1/cos2x

=tan2x-1/cos2x

=sin2x/cos2-1/cos2x

=(sin2x-1)/cos2x

=(sin2x-(sin2x+cos2x))/cos2x

=(sin2x -sin2x-cos2x)/cos2x

=-cos2x/cos2x

=-1