Prove the identity `(sin^2x)/(1 - cos x) = (sec x + 1)/sec x`

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justaguide eNotes educator| Certified Educator

The identity `sin^2 x/(1 - cos x) = (sec x + 1)/sec x` has to be proved.

Start from the left hand side

`(sin^2x)/(1 - cos x)`

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

=> `((1 - cos x)(1 + cos x))/(1 - cos x)`

=> `1 + cos x` ...(1)

Now the left hand side

`(sec x + 1)/sec x`

=> `1 + 1/sec x`

=> `1 + cos x` ...(2)

As (1) and (2) are the same it proves that `(sin^2x)/(1 - cos x) = (sec x + 1)/sec x`