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Expert: Sherry Wallin - 7/11/2011


Question
Prove that
[cos(Theta)/(1-tan(theta)]+[sin (theta)/1-cot(theta)]=Sin(theta)+cos(theta)

Answer
Dhananjay~

Let's call theta x so that we have:
[cos x/(1-tan x]+[sin x/1-cot x]=sin x+cos x


[cos x/(1-tan x]+[sin x/1-cot x]
= [cos x/(1-(sin x)/(cos x)]+[sin x/1-(cos x)/(sin x)]
= cos(cos x)/(cos x)(1-sin x/cos x) + (sin x)(sin x)/(1-cos x/sin x)
= cos^2 x/(cos x - sin x) + sin^2x/(sin x - cos x)
= -cos^2x/(sin x - cos x) + sin^2x/(sin x - cos x)  because -1(cos^2x)/-1(cos x - sin x) = -cos^2x/(sin x - cos x)
= (sin^2x-cos^2x)/(sin x - cos x)
= [(sin x - cos x)(sin x + cos x)]/(sin x - cos x)
= sin x + cos x
= sin(theta) + cos(theta)

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Sherry Wallin

Expertise

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

Experience

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.

Education/Credentials
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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