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Answer 1 · 2016-09-13T19:21:49

See the Proof in Explanation.

The L.H.S.#=(1+coty)/cscy#

#=(1+cosy/siny)/(1/siny)#

#=((siny+cosy)/siny)/(1/siny)#

#=siny+cosy......................(1)#

The R,H.S.#=(1+tany)/secy#

#=(1+siny/cosy)/(1/cosy)#

#=((cosy+siny)/cosy)/(1/cosy)#

#=cosy+siny..........................(2)#

From #(1) and (2)#, we have,

The L.H.S.=The R.H.S.

Alternatively,

The L.H.S.#=(1+coty)/cscy#

#=(1+1/tany)/cscy#

#=(tany+1)/(tanycscy)#

#=(1+tany)/(siny/cosy*cscy)#

#=(1+tany)/(siny*secy*cscy)#

#=(1+tany)/secy...............".[as, "siny*cscy=1]#

=the R.H.S.

Hence, the Proof.