SOLUTION: How do I establish the identity of the following? show steps please 1. sin theta(cot theta + tan theta) = sec theta 2. (sin theta + cos theta)^2 + (sin theta - cos theta)^2

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: How do I establish the identity of the following? show steps please 1. sin theta(cot theta + tan theta) = sec theta 2. (sin theta + cos theta)^2 + (sin theta - cos theta)^2       Log On

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Question 5011: How do I establish the identity of the following? show steps please
1. sin theta(cot theta + tan theta) = sec theta
2. (sin theta + cos theta)^2 + (sin theta - cos theta)^2 = 2
Thanks

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
instead of theta, i will use A..easier to write here

1. sinA(cotA+tanA) = secA
sinAcotA+sinAtanA = secA
sinAcotA+sinAtanA = 1/cosA
cosA(sinAcotA+sinAtanA) = 1
cosAsinAcotA + cosAsinAtanA = 1

right then...tanA = sinA%2FcosA and cotA = cosA%2FsinA, so:

cosAsinAcosA%2FsinA+%2B+cosAsinAsinA%2FcosA+=+1
cosAcosA + sinAsinA = 1
sin%5E2%28A%29+%2B+cos%5E2%28A%29+=+1

2. (sin theta + cos theta)^2 + (sin theta - cos theta)^2 = 2
(sinA + cosA)^2 + (sinA - cosA)^2 = 2
sin^2A + cos^2A + 2sinAcosA + sin^2A + cos^2A - 2sinAcosA = 2
2(sin^2A + cos^2A) = 2
sin^2A + cos^2A = 1

jon.