Prove cofunction idenity using addition and subtraction 1 ta

Prove cofunction idenity using addition and subtraction

1) tanx - tany = (sin(x-y)) / (cos x cos y)

Solution

LHS

tanx - tany

=(sinx/cosx)-(siny/cosy)

=(sinxcosy -cosxsiny)/(cosxcosy)

=(sin(x-y))/(cosx cosy)

=RHS

therefore  tanx - tany = (sin(x-y)) / (cos x cos y)