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Prove the identity:

 (cot x sin x)(sec x – cos x) = sin2x

 

Calculation

 

 

 

 

Reason

 

This follows by the definition of cot x = cos x / sin x and  sec x = 1 / cos x

 

This follows from canceling the sin x  term.

 

This follows multiplying cos x through.

 

This follows from the Pythagorean identity 1 – cos2 x = sin2 x.

 Apr 25, 2021
 #1
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 (cot x sin x)(sec x – cos x)    =

 

(cosx / sinx) (sinx)    ( 1/cosx  - cos x)   =

 

cos x   ( 1  - cos^2 x) / cos x ]   =

 

1 - cos^2 x  =   

 

 sin^2x

 

cool cool cool

 Apr 25, 2021

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