Question

Question #d92c6

Answer 1

Proving the identity will not fit in the answer, so look below.

Explanation:

So, we are trying to prove this: `tanx-cscxsecx(1-2cos^2x)=cotx`
Using this proof: `sin^2 x + cos^2x=1`...
`tanx-cscxsecx(sin^2x+cos^2x-2cos^2x)=cotx`
`tanx-cscxsecx(sin^2x-cos^2x)=cotx`

Using these proofs: `tanx = sinx/cosx`, `cscx=1/sinx` and `secx=1/cosx`.
`sinx/cosx-1/(sinxcosx)(sin^2x-cos^2x)=cotx`
`sinx/cosx-(sin^2x-cos^2x)/(sinxcosx)=cotx`

Make both denominators the same on the left side only... (we leave the right side alone for proofs).
`(sin^2x-(sin^2x-cos^2x))/(sinxcosx)=cotx`
`(sin^2x-sin^2x+cos^2x)/(sinxcosx)=cotx`
`(cos^2x)/(sinxcosx)=cotx`
`(cosx)/(sinx)=cotx`

Use this proof: `cosx/sinx = cotx`
`cotx=cotx`