Trig Identities : Help 3 Questions.

[xLaser]

I can't get these 3 questions, can someone help me?

1. cotB [ (tanA + TanB) / (cotA+cotB) ] = tan A

2. (sin^2A + 2cosA - 1) / (2 + cosA - cos^2A) = 1 / (1+ secA)

3. cos^3A + sin^3A = (cosA+SinA)(1-SinAcosA)

please help out on these, thx in advance. U can write the / sign as fractions cuz i can't do it on the computer here.

[Hurkyl]

For proving trig identities, it's generally useful to convert everything into sin and cos, cross-multiply all fractions, and multiply out all factorizations.

[Diane_]

It's also helpful to know the double-angle formulas and the half-angle formulas.

[xLaser]

no need to use double-angle formulas for those... i just can't figure them out. can someone actually do one?

[kreil]

here is the first one:
1. tan(A)=cot(B)\frac{tan(A) + tan(B)}{cot(A)+cot(B)}

Express in terms of sine and cosine:
=(\frac{\cos{B}}{\sin{B}})\frac{\frac{\sin{A}}{\co s{A}}+\frac{\sin{B}}{\cos{B}}}{\frac{cosA}{sinA}+\ frac{cosB}{sinB}}

Get common denominators and add the top/bottom to form 1 complex fraction:
=(\frac{\cos{B}}{\sin{B}})\frac{\frac{sinAcosB+sin BcosA}{cosAcosB}}{\frac{sinBcosA+sinAcosB}{sinAsin B}}

Simplify:
=(\frac{\cos{B}}{\sin{B}})\frac{\frac{sin(A+B)}{co sAcosB}}{\frac{sin(A+B)}{sinAsinB}}

=\frac{\frac{sin(A+B)}{cosA}}{\frac{sin(A+B)}{sinA }}=\frac{sinA}{cosA}=tanA

Identities used in solution:

cotA=\frac{cosA}{sinA}

tanA=\frac{sinA}{cosA}

sin(A+B)=sinAcosB+cosAsinB

Good luck with the others, I hope this helps you!