Question

"Question27
If A = 30°, verify that : tan 2 A = 2tanA / 1-tan²A
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 289"

Answer 1

Hey there!

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

HELLO DEAR,


GIVEN THAT:-


A = 30°


NOW,


tan(2*30°) = tan60°

= tan60° = √3




2tanA/(1 - tan²A)

= 2tan30°/(1 - tan²30°)

= (2*1/√3) / (1 - 1/3)

= 2/√3/ ( 3 - 1)/3

= 2/√3/2/3

= 2/√3 * 3/2

= √3


I HOPE ITS HELP YOU DEAR,
THANKS