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Question
Given A = 60° and B = 30°,
prove that: tan (A - B) = `(tan"A" – tan"B")/(1 + tan"A".tan"B")`
Solution
LHS = tan(A – B)
= tan (60° – 30°)
= tan30°
= `(1)/(sqrt3)`
RHS = `(tan"A" – tan"B")/(1 + tan 60°. tan 30°)`
= `(tan60° – tan30°)/(1+tan 60°.tan30°)`
= `(sqrt3 – 1/(sqrt3))/(1 + sqrt3(1/sqrt3))`
= `(2)/(2sqrt3)`
= `(1)/sqrt3`
LHS = RHS
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