Question

prove the following identity
Sin³Q + Cos²Q / SinQ + CosQ = 1 - ( sinQ cosQ)​

Answer 1

Answer:

cosQ/1-tanQ +sinQ/1-cotQ = sinQ + cosQ

L.H.S= cosQ/ 1- (sinQ/cosQ) + sinQ/ 1-(cosQ/sinQ)

=cos2Q / (cosQ-sinQ) + sin2Q / (sinQ-cosQ)

=cos2Q / (cosQ-sinQ) - sin2Q / (cosQ-sinQ)

=cos2Q-sin2Q / (cosQ- sinQ)

=(cosQ+sinQ)(cosQ-sinQ) / (cosQ- sinQ)

= cosQ+sinQ

L.H.S=R.H.S

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