Question

tan (A - B) =
tan A-tan B/1+tan A.tan B
and hence deduce that tan (13pu/12)=tan 15°=2–root3​

Answer 1

Answer:

2-√3

Step-by-step explanation:

tan(13π/12) = tan(π+π/12)

⇒tan(13π/12) = tan( π/12)

We know that  π = 180°

⇒π/12 = 180°/12 = 15°

⇒tan(13π/12) = tan(15°)

tan(15°) = tan(45° - 30°)

⇒tan(15°) = $\frac{tan(45) - tan(30)}{1 + tan(45)tan(30)}$

We know that tan(45°)=1 and tan(30°)=1/√3

substituting the values,

tan(15°) = $\frac{1 - 1/\sqrt{3} }{1 + 1/\sqrt{3}}$

⇒tan(15°) = $\frac{\sqrt{3}- 1}{\sqrt{3}+1 }$

Multiplying the numerator and denominator by √3 - 1,

tan(15°) = $\frac{(\sqrt{3}-1) ^{2} }{(\sqrt{3}+1) (\sqrt{3} -1) }}$

⇒tan(15°) = $\frac{4-2\sqrt{3}}{2}$

⇒tan(15°) = 2 - √3