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My name is Donny and I'm prepping to take my ACTS in a few weeks. I got a bit stumped on these two problems and was hoping you could help (they are very similar, so I thought I could include them both, if that's alright).

I am asked to verify each of these identities
#1 csc^(2)x(1-cos^(2)x)= 1
#2 sec(theta)-sin(theta)*tan(theta)=cos(theta)

I was hoping you could just go through those two problems briefly; explain your answer and how you got them. They are similar problems, but different enough that I wanted to get the processes of both from you.

Thank you for your time.

It is very useful to convert all terms to sin and cos.

#1 Since csc(x) is 1/sin(x) the cscē(x) is 1/sinē(x).
It is known that sinē(x) + cosē(x) = 1, so 1 - cosē(x) = sinē(x).
Putting these two in gives (1/sinē(x))sinē(x), and that reduces to 1.

#2 Put T in for theta and get sec(T) - sin(T)*tan(T).
Since sec(T) = 1/cos(T) and tan(T) = sin(T)/cos(T), we have 1/cos(T) - sin(T)sin(T)/cos(T).
Note that sin(T)sin(T) is sinē(T).
Also not the fractions can be combined.  This gives (1-sinē(T))/cos(T).

Since sinē(T) + cosē(T) = 1, 1 - sinē(T) = cosē(T), so this is cosē(T)/cos(T).
That reduces to cos(T), which is what's on the right.

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Scott A Wilson


I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?


Experience in the area; I have tutored people in the above areas of mathematics for over two years in I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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