Prove the identity cot x 1 cos 2x sin 2x Note that each St

Prove the identity. cot x (1 - cos 2x) = sin 2x Note that each Statement must be based on a Rule chosen from the Rule menu. To see a select the corresponding question mark.

Solution

cotx(1-cos2x)=sin2x
let us simplify the left side
cos(2x) = 2cos²(x) - 1
so we get:
cotx(1-(2cos²(x) - 1))
cotx(1-2cos²(x) +1)
cotx(2-2cos²x)
let us take 2 common
cotx(2(1-cos²x))
now we know that 1-cos²x=sin²x
so let us replace 1-cos²x by sin²x
cotx(2sin²x)
now cotx=cosx/sinx
(cosx/sinx)(2sin²x)
so we get
2sin²xcosx/sinx
so one sinx will cancel out and we will be left with 2sinxcosx which is equal to sin2x
so left hand side is equal to right hand side
hence proved.