Simplifying Trigonometric Equations

[ptsoccerboy]

Hello, I am having trouble with two problems involving double and half angle formulas for trig equations

Prove equation is an identity:
(1 +sinA - cos2A)/(cosA + sin2A)

=(1 + sinA - 1 + sin^2A)/(cosA + 2sinAcosA)

I know that there are three possibilities for the cosine double angle: cos^2A - sin^2A, 1 - sin^2A, and cos^2A - sin^2A but I don't know which one to use.

Also (same instructions)

((1 + tan^2x)(1 - cos^2x))/2
=((1 + tan^2x)(2sin^2x))/2

I'm stuck after that
Please help. Thank you

 

[tkhunny]

Hello, I am having trouble with two problems involving double and half angle formulas for trig equations

=(1 + sinA - 1 + sin^2A)/(cosA + 2sinAcosA)

I know that there are three possibilities for the cosine double angle: cos^2A - sin^2A, 1 - sin^2A, and cos^2A - sin^2A but I don't know which one to use.

1) Please check your three formulas for cos(2A). You're missing a couple of things.

2) This last form is SO close!!

=(1 + sinA - 1 + 2sin^2A)/(cosA + 2sinAcosA) = (sinA + 2sin^2A)/(cosA + 2sinAcosA)

Factor sin(A) out of the numerator and cos(A) out of the denominator.