SOLUTION: Verify the identity with steps: (sin3x)/(sinxcosx)=4cosx-secx

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Question 611752: Verify the identity with steps: (sin3x)/(sinxcosx)=4cosx-secx
Answer by lwsshak3(11628) About Me  (Show Source):
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Verify the identity with steps: (sin3x)/(sinxcosx)=4cosx-secx
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Start with left side:
(sin3x)/(sinxcosx)
=sin(2x+x)/(sinxcosx)
=(sin2xcosx+cos2xsinx)/(sinxcosx)=(2sinxcosxcosx+cos2xsinx)/(sinxcosx)
=2cosx+[(cos2xsinx)/(sinxcosx)]=2cosx+cos2x/cosx=2cosx+[(cos^2x-sin^2x)/cosx]
=2cosx+cosx-(sin^2x)/cosx)
=2cosx+cosx-1+cos^2x)/cosx)
=2cosx+cosx-1/cosx+cosx
=4cosx-1/cosx
=4cosx-secx
verified:
left side=right side