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Question
prove that:
tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`
Sum
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Solution
RHS,
`(2 tan^2 30°)/(1 – tan^2 30°) = (2 (1)/sqrt3)/(1– 1/3) = (2/sqrt3)/(2/3) `
= `2/sqrt3 ÷ 2/3`
= `cancel2/sqrt3 xx3/cancel2`
= `3/sqrt3 = (sqrt3 xx (cancelsqrt3))/cancelsqrt3 `
= `sqrt3`
LHS,
tan (2 x 30°) = tan 60° = `sqrt3`
LHS = RHS
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Chapter 21: Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals] - EXERCISE 21 (C) [Page 322]
