SOLUTION: Verify the identity (1/ tanƟ + cotƟ) = sinƟ cosƟ Can you please help me ? Thanks so much in advance:)

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Question 870188: Verify the identity
(1/ tanƟ + cotƟ) = sinƟ cosƟ
Can you please help me ? Thanks so much in advance:)
Answer by b.uzsoki(1) About Me  (Show Source):
You can put this solution on YOUR website!
1/ (tanx+cotx)
1.Use reciporcal identity tanx=sinx/cos and quotient identity cotx=cosx/sinx to replace tanx and cotx
=1/((sinx/cosx)+(cosx/sinx))
2.Multiply numerators and denominator by common denominator so that you can add the fractions.
=1/((Sinx*Sinx/Cosx*Sinx)+(Cosx*Cosx/Cosx*Sinx))
3. Multiply numerator in two fractions then add the fraction together.
=1/((sin^2x+cos^2x)/(Cosx*Sinx))
4. Sin^2x+Cos^2x=1 is a pythagorean identity. Replace Sin^2x+Cos^2X with "1"
=1/(1)/(Cosx*Sinx)
5.Flip and multiply your fraction
=1*((Cosx*Sinx)/1)
=Cosx*Sinx