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Expert: Sherry Wallin - 8/21/2011


Question
I have a worksheet for homework and out of 7 I don't get these two. Please help, thanks


Verify the identities:

1.  cos^2(X)-sin^2(x)=1-2sin^2(x)



2.tan^2(x)=5=sec^2(x)+4

Answer
Merlene~

Since the cos^2(x) + sin^2(x) = 1, then solving for sin^2(x) you get that cos^2(x) = 1 - sin^2(x) now substitute that into cos^2(x) in your problem:
cos^2(X)-sin^2(x)=1-2sin^2(x) => 1-sin^2(x) - sin^2(x) = 1-2sin^2(x) as desired

for #2 just subtract 4 from both sides getting tan^2(x) + 1 = sec^2(x) and that is one of the original identities

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Sherry Wallin

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I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

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I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

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I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

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Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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