Question

if tan(A+B) = root 3, tan (A-B) = 1/ root 3. Find A and B
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Answer 1

Solution :-

Given ,

• tan ( A + B ) = √3
• tan ( A - B ) = 1/√3

We need to find ,

• ∠A = ?
• ∠B = ?

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• tan ( A + B ) = √3 …eq(1)

• tan ( A - B ) = 1/√3 …eq(2)

Taking Equation 1 & simplifying ,

→ tan ( A + B ) = √3

Substituting √3 = tan60°

→ tan ( A + B ) = tan60°

→ A + B = 60°

→ A = 60° - B …eq(3)

Taking Equation 2 & simplifying

→ tan ( A - B ) = 1/√3

Substituting 1/√3 = tan30°

→ tan ( A - B ) = tan30°

→ A - B = 30°

→ A = 30° + B …eq(4)

Now , from eq 1 & 2

⇒ 60° - B = 30° + B

⇒ 60° - 30° = B + B

⇒ 30° = 2B

⇒ B = 30°/2

⇒ ∠B = 15°

Now , substituting the value of ∠B in eq(3)

⇒ A = 60° - 15°

⇒ ∠A = 45°

Hence , ∠A = 45° & ∠B = 15°