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Use the following notation angle = `alpha` .
You need to prove the identity `cos alpha*(sec alpha - csc alpha) = 1 - cot alpha`
You should replace `sec alpha` by `1/cos alpha` and `csc alpha` by `1/sin alpha` .
The left side becomes: `cos alpha*(1/cos alpha - 1/sin alpha).`
Bringing the terms in the brackets to a common denominator yields:
`(cos alpha*(sin alpha - cos alpha))/(cos alpha*sin alpha).`
Reducing by `cos alpha` yields:
`(sin alpha - cos alpha)/sin alpha`
Opening the brackets yields: `sin alpha/sin alpha - cos alpha/sin alpha`
The ratio `cos alpha/sin alpha` denotes the cotangent function, therefore `sin alpha/sin alpha - cos alpha/sin alpha = 1 - cot alpha.`
This final result proves that the identity is checked.
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