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Luna Moreno
Mathematics
26 January, 16:45
Verify the identity:
(1-sinx) / cosx = cosx / (1+sinx)
+2
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Julio Lyons
26 January, 17:07
0
For the answer to the question above,
Let's work with the left-hand side
We're going to times cosx/1-sinx by 1+sinx/1+sinx, you can do this because 1+sinx/1+sinx is equal to 1, so you aren't really changing anything.
After you've times the top and bottom by 1+sinx, you get:
cosx (1+sinx) / (1-sinx) (1+sinx)
The denominator is a difference of squares, so you get 1-sin^2 x
what you have now is
cosx (1+sinx) / 1-sin^2x
You know that 1-sin^2x is equal to cos^2x
so know you have
cosx (1+sinx) / cos^2x
get rid of the cosx on top by simplifying and the cos^2x so that you're left with
(1+sinx) / cos x
Therefore cosx / 1 - sinx = 1 + sinx / cos x
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