Question
Verify the identity.
(csc(2x) - sin(2x))/cot(2x)=cos(2x)
=csc(2x)/cot(2x) - sin(2x)/cot(2x)
=csc(2x)/cot(2x) - cos(2x)
Is this correct so far? If so then how would I continue? I got stuck on this part...
(csc(2x) - sin(2x))/cot(2x)=cos(2x)
=csc(2x)/cot(2x) - sin(2x)/cot(2x)
=csc(2x)/cot(2x) - cos(2x)
Is this correct so far? If so then how would I continue? I got stuck on this part...
Answers
Oops.
sin/cot = sin*tan = sin^2/cos
csc/cot = 1/sin * sin/cos = 1/cos
You should have said
csc(2x)/cot(2x) - sin(2x)/cot(2x)
= 1/cos(2x) - sin^2(2x)/cos(2x)
= (1-sin^2(2x))/cos(2x)
= cos^2(2x)/cos(2x)
= cos(2x)
or, csc-sin = (1-sin^2)/sin = cos^2/sin = cos * cot
sin/cot = sin*tan = sin^2/cos
csc/cot = 1/sin * sin/cos = 1/cos
You should have said
csc(2x)/cot(2x) - sin(2x)/cot(2x)
= 1/cos(2x) - sin^2(2x)/cos(2x)
= (1-sin^2(2x))/cos(2x)
= cos^2(2x)/cos(2x)
= cos(2x)
or, csc-sin = (1-sin^2)/sin = cos^2/sin = cos * cot
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