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(sec(x)-1) * (sec(x)+1)* cot(x) = tan(x)

 Jun 13, 2017
 #1
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+1

use the identity (a+b)(a-b) = a^2  - b^2  with {(sec x)-1}{ (sec x +1) }   to get

sec^2(x)  -  1

we can now write expression as

{sec^2(x) -1} * cot (x)    

and use the trig identity  sec^2(x) - 1   = tan^2(x)    to get expression as

tan^2(x)*cot(x)   = tan^2(x) * {1/tan(x)}     = tan(x)

 Jun 13, 2017
 #2
avatar+7373 
+2

\(\text{LHS}\\ =(\sec x - 1)(\sec x + 1)(\cot x) \\ =(\sec^2 x - 1)(\cot x)\\ =(\tan^2 x)(\cot x)\\ =\tan x\\ =\text{RHS}\)

.
 Jun 13, 2017

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