1. ## Simplifying trigonometric functions

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?

2. Originally Posted by aikenfan
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 $cos^2 x = y$

$y - sin^2 x = 2y - 1$

$y - 2y - sin^2 x = -1$

$-y - sin^2 x = - 1$

[Multiply by -1]

$y + sin^2 x = 1$

$But \ y = cos^2 x$

$cos^2 x + sin^2 x = 1$

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Your solution to number 7 was a bit elaborate.

Simply say:

$tan^2 x + 5 - 4 = sec^2 x$

$tan^2 x + 1 = sec^2 x$

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Number 8 also seems fine. (EDIT: Except you left out a negative sign on the RHS! )

3. What do I do to finish 7, bc the original equation was
tan^2x + 5 = sec^2x + 4

but I have only got:
tan^2x + 1 = sec^2x

4. Originally Posted by aikenfan
What do I do to finish 7, bc the original equation was
tan^2x + 5 = sec^2x + 4

but I have only got:
tan^2x + 1 = sec^2x
But that is an identity...

Oh i think i know what you mean:

$tan^2x + 1 = sec^2x$

$\frac{sin^2 x}{cos^2 x} + 1 = \frac{1}{cos^2 x}$

[Multiply straight through with $cos^2 x$]

5. For number 8:

$

1 - \frac{1}{sin^2 x} = \frac{cos^2 x}{sin^2 x}
$

[Multiply straight through with $sin^2 x$ here]

Just check your Number 8, seems like you left out a negative sign on the right hand side.

6. 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.

7. Originally Posted by aikenfan
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.
You're right, you are confusing me.

$sin^2 x + cos^2 x = 1$

For any value of $x$, you will get:

$1 = 1$