| Trigonometric Identities |
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| Prove that : {[cos(-x)]/[sec(-x) + tan(-x)]} = 1 + sin x Proofing : Consider the left hand side only : cos(-x)/[sec(-x)+tan(-x)]= =cos(x)/[sec(x)-tan(x)]= =cos(x)/[1/cos(x)-sin(x)/cos(x)]= =cos(x)/[{1-sin(x)}/cos(x)]= =cos(x)*cos(x)/[1-sin(x)]= =cos^2(x)/[1-sin(x)]= =[1-sin^2(x)]/[1-sin(x)]= =[1-sin(x)]*[1+sin(x)]/[1-sin(x)]= =1+sin(x) to be proved since this result equals to the right hand side of the problem. |
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