Question

if x+y=z and tanx=ktany, prove that sin z = [(k+1)+(k-1) sin]sin(x-y)

Answer 1

tan x = k tan y

  ( sin x ) / ( cos x ) = k ( sin y ) / ( cos y )

  ( sin x cos y ) / ( cos x sin y ) = k / 1

  ( sin x cos y + cos x sin y ) / ( sin x cos y - cos x sin y ) = ( k + 1 ) / ( k - 1 )

[ sin (x+y) ] / [ sin (x-y) ] = ( k + 1 ) / ( k - 1 )

( k - 1 ) sin (x+y) = ( k + 1 ) sin (x-y) ...

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