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Advanced Math/pre-cal - verifying identities

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Expert: - 4/19/2009


Question
Please help - think I got this one but need to be sure

1 + sin x = cos x / (sec x - tan x)

Thanks so much!!!!

Answer
I don't worry about the space.  
I assume sinx is sin x, cosx, secx is sec x and tanx is tanx.
I have even dealt with people where sinxcosxsinx is really
sin˛xcosx.  It may take a little reading to understand this,
but it sure makes it easier to type and holds the problem together better.  That said, lets have at the problem.

I'll start with the right hand side of the equation.

It is known that secx is 1/cosx.

It is also known that tanx is sinx/cosx.

That said, the fraction can be said to be
cosx/(1/cosx - sinx/cosx) = cosx/((1-sinx)/cos) = cos˛x /(1-sinx).

It is known that cos˛x = 1 - sin˛x, so this is (1-sin˛x)/(1-sinx).

From algebra, we know that 1 - sin˛x = (1+sinx)(1-sinx),
so when we divide by (1-sinx) all we get is the left hand side.

Start with right, end with left, ... is that good?

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