Question

2 tan 30°/
1- tan2 30°​

Answer 1

Answer:

tan 60

Step-by-step explanation:

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Answer 2

★ Solution :-

We need to find ,

• 2tan30°/1 - tan²30°

There are two types of solving

Method 1 :- By comparing with the formula

Method 2 :- Using the value of tan30°

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Method 1 :-

As we know that

tan2A = 2tanA / 1 - tan²A

Now , comparing with the given question

→ 2tan30°/1 - tan²30°

That's equal to tan[ 2( 30° ) ] = tan60°

Now ,

→ 2tan30°/1 - tan²30° = tan60°

As we know that tan60° = √3

So ,

→ 2tan30°/1 - tan²30° = √3

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Method 2 :-

As we know that

tan30° = 1/√3

Substituting we have ,

→ 2(1/√3)/1 - (1/√3)²

→ ( 2/√3 )/1 - ( 1/3 )

→ ( 2/√3 )/( 3 - 1 )/3

→ (2/√3)/2/3

→ ( 1/√3 )/( 1/3 )

→ 1/√3 × 3

→ 3/√3

By rationalising the denominator

→ 3/√3 × √3/√3

→ 3√3/3

→ 2tan30°/1 - tan²30° = √3

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Hence , 2tan30°/1 - tan²30° = √3