Prove this trigonometric identity

May 2010
64
0
Palmy
Can somebody show me the steps to prove this question.

Prove that:

cos x + cos x = 2sec x
1 - sin x 1 + sin x
 
Dec 2009
1,506
434
Russia
{cosx}/{1-sinx} + {cosx}/{1+sinx} = {(cosx)(1+sinx)+(cosx)(1-sinx)}/{(1-sinx)(1+sinx)}=

={(cosx)(1+sinx)+(cosx)(1-sinx)}/{(1-(sinx)^2}=

={(cosx)(1+sinx)+(cosx)(1-sinx)}/{(cosx)^2}=

={(1+sinx)+(1-sinx)}/{(cosx)}=

={2}/{cosx}=

=2secx
 
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skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
Can somebody show me the steps to prove this question.

Prove that:

cos x + cos x = 2sec x
1 - sin x 1 + sin x
working on the left side, get a common denominator ...

\(\displaystyle (1-\sin{x})(1+\sin{x}) = 1-\sin^2{x} = \cos^2{x}\)

... then add the two fractions.
 
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