Question

Verify that sin2x=2cotsin^2x is an identity

Answer 1

Explanation:

sin^2x = 2cotx sin^2x

Rewrite right side as fractions:

sin^2x =
`(2)/(1)` *
`(cosx)/(sinx)` *
`((sinx)(sinx))/(1)`

Multiply together
`(cosx)/(sinx)` and
`((sinx)(sinx))/(1)` :

sin^2x =
`(2)/(1)` *
`((cosx)(sinx)(sinx))/(sinx)`

Cancel out sinx on top and bottom:

sin^2x =
`(2)/(1)` *
`((sinx)(cosx))/(1)`

Multiply together 2 and (sinx)(cosx):

sin^2x = 2sinxcosx

Substitute sin^2x in for 2sinxcosx:

sin^2x = sin^2x

Answer 2

Vertify is an identity

Sin2x=2cotx(sin^2x)

starting from the right-hand side

2cotx(sin^2x)

=2(cosx/sinx)(sin^2x)

=2(cosx/sinx)(sin^2x)

=2sinxcosx=sin2x

ans:right-hand side=left-hand side

Explanation: