Proof of a Trigonometric Identity
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Verify or Prove the identity: (sin x + cos x + 1)/(sin x + cos x - 1) = (csc x)(sec x) + csc x + sec x + 1
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Solution Summary
The identity is proved from LHS to RHS.
LHS = (sin x + cos x + 1)/(sin x + cos x - 1)
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LHS = (sin x + cos x + 1)/(sin x + cos x - 1)
Multiply and divide by sin x + cos x + 1. Then
LHS = (sin x + cos x + 1)/(sin x + cos x - 1) * (sin x + cos x + 1)/(sin x + cos x + 1)
= (sin x + cos x + ...
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