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Question
Find the value of x, if tan x = `(tan60^circ - tan30^circ)/(1 + tan60^circ tan30^circ)`
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Solution
tan x = `(tan60^circ - tan30^circ)/(1 + tan60^circ tan30^circ)`
tan x = `(sqrt3 - 1/sqrt3)/(1 + sqrt3 xx 1/sqrt3)`
tan x = `((3 - 1)/sqrt3)/(1 + 1)`
= `2/(2sqrt3)`
= `1/sqrt(3)`
= tan 30°
Hence, x = 30°
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