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verify identity

sin(X)sec(x)=1-(cos^2)x/sin(X)cos(X)

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
4.9 4.9 (408 lesson ratings) (408)
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You need the following two identities for this problem:
 
sec(x) = 1/cos(x)
sin2x + cos2x = 1
 
Now let's use them in your problem:
 
sin(x)sec(x) = [1-cos2(x)]/sin(x)cos(x)
 
sin(x)/cos(x) = sin2(x)/sin(x)cos(x)       [sec(x) = 1/cos(x), 1-cos2(x)=sin2(x)]
 
sin(x)/cos(x) = sin(x)/cos(x)
 
QED