Hi! I have started on several of these problems, but I am having a really hard time with them...could anyone please look over my work?
Number 5 seems fine.
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For Number 6:
This one really isn't hard.
Let's set $\displaystyle cos^2 x = y$
$\displaystyle y - sin^2 x = 2y - 1$
$\displaystyle y - 2y - sin^2 x = -1$
$\displaystyle -y - sin^2 x = - 1$
[Multiply by -1]
$\displaystyle y + sin^2 x = 1$
$\displaystyle But \ y = cos^2 x$
$\displaystyle cos^2 x + sin^2 x = 1$
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Your solution to number 7 was a bit elaborate.
Simply say:
$\displaystyle tan^2 x + 5 - 4 = sec^2 x $
$\displaystyle tan^2 x + 1 = sec^2 x $
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Number 8 also seems fine. (EDIT: Except you left out a negative sign on the RHS! )
For number 6, I am supposed to turn the left side of the equation and turn it into the right side, using Quotient properties, etc...that is where I am stuck...I am not quite following...sorry for any confusion...I am having a really hard time with these...I don't think that I am done on 5 yet, because the left side is not equal to the right side.