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# Trigonometry Identities

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1. prove:

cosecx / cosecx - sinx = sec^2x

LHS= (1/sinx)/ (1/sinx)-sinx/1

= sinx/ sin2x

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

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

where do i go from here?
2. (Original post by Custardcream000)
prove:

cosecx / cosecx - sinx = sec^2x

LHS= (1/sinx)/ (1/sinx)-sinx/1

= sinx/ sin2x

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

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

where do i go from here?
= sinx/ sin2x

I'm not sure where this came from.

Try multiplying top and bottom of the fraction by sin(x) instead.

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