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help with tan x question

 
how do I prove that tan  x (cot x + tan x) = sec^2 x
 
thank you

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
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tan(x)[cot(x) + tan(x)] = sec2(x)
 
Identity: cot(x) = 1/tan(x)
 
tan(x)[(1/tan(x)) + tan(x)] = sec2(x)
 
tan(x)/tan(x) + tan2(x) = sec2(x)
 
1 + tan2(x) = sec2(x)
 
which is a Pythagorean identity.