Question

Prove that 1 - cosx / sinx = sinx / 1 + cosx
how?

Answer 1

see explanation

Explanation:

using the identity

cos²x = 1 - sin²x

consider the left side

`(1-cosx)/(sinx)`

multiply numerator/ denominator by (1 + cosx)

=
`((1-cosx)(1+cosx))/(sinx(1+cosx))` ← expand numerator

=
`(1-cos^2x)/(sinx(1+cosx))`

=
`(sin^2x)/(sinx(1+cosx))` ← cancel sinx on numerator/ denominator

=
`(sinx)/(1+cosx)`

= right side , thus proven