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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.