sinx-sin y-ycosx +cos y18.- tan2

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Solution

The given trigonometric equation is,

sinx−siny cosx+cosy =tan x−y 2

Solve left hand side,

L.H.S.= sinx−siny cosx+cosy = [ 2cos( x+y 2 )sin( x−y 2 ) ] [ 2cos( x+y 2 )cos( x−y 2 ) ] = [ sin( x−y 2 ) ] [ cos( x−y 2 ) ] =tan( x−y 2 )

Right hand side is,

R.H.S.=tan( x−y 2 )

Hence, L.H.S.=R.H.S.

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