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Expert: Sherman D. - 5/28/2008


Question
Hi
I have this qusetion I need the answer very quickly.
Can you prove that Cos^4(theta)+sin^2(theta) is equal to 2Cos^2(theta)-1
thank you

Answer
cos(A)^4 + sin(A)^2 = 2cos(A)^2 - 1

cos(A)^4 + (1 - cos(A)^2) = 2cos(A)^2 - 1
cos(A)^4 + 1 - cos(A)^2 = 2cos(A)^2 - 1
cos(A)^4 - cos(A)^2 + 1 = 2cos(A)^2 - 1
cos(A)^4 - 3cos(A)^2 + 2 = 0

(cos(A)^2 - 1)(cos(A)^2 - 2) = 0

cos(A)^2 - 1 = 0
cos(A)^2 = 1
cos(A) = -1 or 1
A = pi or 0

cos(A)^2 - 2 = 0
cos(A)^2 = 2
cos(A) = -sqrt(2) or sqrt(2)
A = which gives you an invalid answer, so

cos(A)^4 + sin(A)^2 = 2cos(A)^2 - 1

if and only if A = 180(n - 1)

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Sherman D.

Expertise

I can answer questions dealing in mathematics of all kinds except for Physics and Calculus, but i can answer questions in Pre-Calculus and Chemistry. I can also answer questions in Recipes of all kinds. I can find games cheats/walkthroughs, but i can`t find a specific game online or offline. I can also do history and recipes for alcoholic beverages.

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Mathematics, Recipes, History, and Games.

Education/Credentials
High School graduated. I graduated with honors, and i was in Beta Club for a year and a half.

Awards and Honors
Principle's list and A and B honor roll in high school only.

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