As far as I can tell, exactly nothing you've done here is correct. For one thing, I'm very confused because you say "I decided to manipulate the

**right** side" but then begin by saying that the

**left** hand side is equal to something. I can explain that away as a typo somewhere, although I can't be certain where. However, neither the left-hand nor the right-hand side is equal to [tex][\cos(g) - \cos(h)]^2[/tex].

If we let [tex]\alpha = \cos(g)[/tex] and [tex]\beta = \cos(h)[/tex], it should become clear why the right-hand side is not equal to this, because [tex]\alpha^2 - \beta^2 \ne (\alpha - \beta)^2[/tex]. And using the

**angle addition and subtraction formulas** reveal that the left-hand side is not equal to this either.

[tex]\cos(g+h) \cos(g-h) = [\cos(g) \cos(h) - \sin(g) \sin(h)][\cos(g) \cos(h) + \sin(g) \sin(h)] = \cos^2(g) \cos^2(h) - \sin^2(g) \sin^2(h)[/tex]

This, too, seems to be plagued by strange notation, wherein you say you're manipulating the right-hand side, but then actually manipulate the left-hand side. I'm also guessing there was another typo and you actually meant the right-hand side to be [cos(x) - 1][

**sin**(x) - 1]. That change makes it actually be an identity. In any case, your first step is good, but after that it's not correct due to math errors. I can't see how you got from:

[tex]\left[ \sin(x) - \dfrac{\sin(x)}{\cos(x)} \right] \left[\cos(x) - \dfrac{\cos(x)}{\sin(x)} \right][/tex]

To:

[tex]\dfrac{1}{\cos(x)} \cdot \dfrac{1}{\sin(x)}[/tex]

I assume you tried to follow the usual steps of multiplying by a form of 1 (in this case [tex]\dfrac{\cos(x)}{\cos(x)}[/tex]) to get a common

denominator... but then what?

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