Trigonometry Identities Proving

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

Trigonometry Identities Proving

Postby Guest » Sat Oct 15, 2016 2:37 pm

Prove that SinA/1-CotA + Cos A/1 - Tan A = CosA + Sin A
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Re: Trigonometry Identities Proving

Postby Guest » Wed Oct 19, 2016 3:15 am

cotA = cosA/sinA

tanA = sinA/cosA


[tex]\frac{sinA}{1-cotA} = \frac{sinA}{\frac{sinA - cosA}{sinA}} = \frac{sin^2A}{sinA - cosA}[/tex]

[tex]\frac{cosA}{1-tanA} = \frac{cosA}{\frac{cosA - sinA}{cosA}} = \frac{cos^2A}{cosA - sinA}[/tex]

[tex]\frac{sin^2A}{sinA - cosA} + \frac{cos^2A}{cosA - sinA} = \frac{sin^2A}{sinA - cosA} - \frac{cos^2A}{sinA - cosA} =[/tex]
[tex]=\frac{sin^2A - cos^2A}{sinA - cosA} = \frac{(sinA - cosA)(sinA + cosA)}{sinA - cosA} = sinA + cosA[/tex]
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