We know that Tan α = xsin β 1 − xcos β, Tan β = ysin α 1 − ycos α, and prove that sin α sin β = XY

It is proved that: Tan α = sin α, cos α = xsin β 1 − xcos β, Tan β = sin β, cos β = ysin α 1 − ycos α, ∵ cos α sin α = 1 − xcos β, xsin β cos β sin β = 1 − ycos α ysin α. By subtracting the two formulas, cos α sin α - cos β sin β = 1xsin β − cos β sin β - (1ysin α − cos α sin α), ∵ 1ysin α = 1xsin β, ∵ xsin β = ysin α, ∵ sin α sin β = XY

We know that Tan α = xsin β 1 − xcos β, Tan β = ysin α 1 − ycos α, and prove that sin α sin β = XY

We know that Tan α = xsin β 1 − xcos β, Tan β = ysin α 1 − ycos α, and prove that sin α sin β = XY

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