SOLUTION: This is proving a trigonometric equation.
Verify cos(x))/(1-sin(x))=sec(x)+tan(x)
All I can figure out is how to expand it somewhat to be
cos(x)/(1-sin(x)=(1/cos(x))+(sin(x
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Question 307241: This is proving a trigonometric equation.
Verify cos(x))/(1-sin(x))=sec(x)+tan(x)
All I can figure out is how to expand it somewhat to be
cos(x)/(1-sin(x)=(1/cos(x))+(sin(x)/cos(x) I have no clue where to go now.
Please help.
Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
}{1-\sin(x)} = \sec(x)+\tan(x))
... Start with the given equation.
We're only going to manipulate the left side.
(1+\sin(x))}{(1-\sin(x))(1+\sin(x))} = \sec(x)+\tan(x))
... Multiply both numerator and denominator of the left side by )
Think of of the last step as rationalizing the denominator.
(1+\sin(x))}{1-\sin^2(x)} = \sec(x)+\tan(x))
... FOIL
+\cos(x)\sin(x)}{1-\sin^2(x)} = \sec(x)+\tan(x))
... Distribute
+\cos(x)\sin(x)}{\cos^2(x)} = \sec(x)+\tan(x))
... Replace )
with )
}{\cos^2(x)}+\frac{\cos(x)\sin(x)}{\cos^2(x)} = \sec(x)+\tan(x))
... Break up the fraction.
}+\frac{\sin(x)}{\cos(x)} = \sec(x)+\tan(x))
... Cancel out like terms.
+\tan(x) = \sec(x)+\tan(x))
... Use the identities }=\sec(x))
and }{\cos(x)}=\tan(x))
Since the two sides are identical, this verifies the identity.
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