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Simplifying Trigonometric Expressions

Sin q/cos q+ cos q/ sin q=

sin(a+b) cos b -cos (a+b) sin b

Solution This solution is FREE courtesy of BrainMass!

Solution.

(1) sin q/cos q+ cos q/ sin q
=(sinq)^2/(cosq*sinq)+(cosq)^2/(cosq*sinq)
=[(sinq)^2+(cosq)^2]/(cosq*sinq)

Use an identity: (sinq)^2+(cosq)^2=1. We have
sin q/cos q+ cos q/ sin q
=(sinq)^2/(cosq*sinq)+(cosq)^2/(cosq*sinq)
=[(sinq)^2+(cosq)^2]/(cosq*sinq)
=1/(cosq*sinq)
=2/sin(2q)

(2) sin(a+b) cos b -cos (a+b) sin b

Using a formula: sin(x-y)=sinx cosy-cosx siny, where x=a+b and y=b, we have
sin(a+b) cos b -cos (a+b) sin b
=sin[(a+b)-b]
=sin(a)