calculate the value of tan[pi/2+pi/6]
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When seeing such a question, students usually adopt the tan (A+B) formula, but that method requires the value of tan π/2 which is ∞. Therefore, I will adopt a simpler method.
Let us add the terms given in the bracket.
Tan (π/2 + π/6)
= Tan (3π/6 + π/6)
= Tan (4π/6)
= Tan (2π/3)
= Tan (120°)
We can write Tan 120° as Tan (180-60)°
We know that Tan (180-θ) = - Tan θ as it lies in the second quadrant.
Hence, Tan (180-60)° = - Tan 60°
Tan 60° = √3
- Tan 60° = - √3
Therefore, -√3 is the required answer.
Let us add the terms given in the bracket.
Tan (π/2 + π/6)
= Tan (3π/6 + π/6)
= Tan (4π/6)
= Tan (2π/3)
= Tan (120°)
We can write Tan 120° as Tan (180-60)°
We know that Tan (180-θ) = - Tan θ as it lies in the second quadrant.
Hence, Tan (180-60)° = - Tan 60°
Tan 60° = √3
- Tan 60° = - √3
Therefore, -√3 is the required answer.
Róunak:
Nice one
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