Question 870188
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