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Question
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
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Solution
It is given that A = 60°, B = 30°
Putting A = 60° and B = 30° in the given equation,
we get
tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`
⇒ tan( 60° - 30° ) = `(tan 60° - tan 30° )/(1 + tan 60°. tan 30° )`
⇒ tan 30° = `(sqrt3 - 1/sqrt3)/(1 + sqrt3 xx 1/sqrt3)`
⇒ `((3-1)/sqrt3)/2`
⇒ `(2/sqrt3)/(2/1)`
⇒ `2/(2sqrt3)`
⇒ `1/sqrt3`
⇒ LHS = RHS
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