Question

If A=30° verify that:
tan2A=2tanA/1-tan2A

Answer 1

Given to verify : tan2A = 2 tan A / 1 - tan²A

If A = 30°

1) tan 2A = tan(2*30) = tan60 = √3 [ T - Ratio of 60° , π/3 ]
2) tanA = tan30 = 1/√3

Now,
Given equation to verify : tan2A = 2 tan A / 1 - tan²A

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Finding the value of tan2A

= tan60

= √3

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Finding the value of 2 tan A / 1 - tan²A

= 2 tan30 / 1 +tan²30

= 2(1/√3 ) / 1 - (1/√3)²

= 2/√3 / ( 1 - 1/3 )

= 2/√3 / 2/3

= 2/√3 * 3/2

= 3/√3

= √3

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Here, We observe that tan2A = 2 tan A / 1 - tan²A

Hence proved that, tan2A = 2 tan A / 1 - tan²A for A = 30°

Answer 2

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