Verify the identity: (secx - tanx) (cscx + 1) = cotx

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Verify `(secx-tanx)(cscx+1)=cotx` :

Rewrite all terms in terms of sin and cos:

`=(1/(cosx)-(sinx)/(cosx))(1/(sinx)+1)`     combine fractions:

`=((1-sinx)/(cosx))((1+sinx)/(sinx))`          multiply fractions:

`=(1-sin^2x)/(cosxsinx)`                        use the pythagorean identity:

`=(cos^2x)/(cosxsinx)`                       cancel common factor:

`=cosx/sinx`

`=cotx` as required.

Sources:

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