Question

using tan theta minus phi is equal to tan theta minus tan phi whole upon 1 + tan theta into 10 phi. Evolute and simplify tan 13 Pi upon 12.




Guys plz answer correctly don't be wrong otherwise I report that one........

Answer 1

tan(13π/12) = tan(π + π/12)

we know that tan(π + θ) = tanθ

⇒ tan(π + π/12) = tan(π/12)

⇒ tan(π/12) = tan(15°)   (converted angle in radians to angle in degrees)

⇒ we need to find the value of tan(15°)

we know that 15° can be written as 45° - 30°

⇒  tan(15°) = tan(45° - 30°)

we know that tan(A - B) = (tanA - tanB)/(1 + tanA.tanB)

⇒ tan(45° - 30°) = (tan45° - tan30°)/(1 + tan45°.tan30°)

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

⇒ tan(15°) = (1 - 1/√3)/(1 + 1/√3)

⇒ tan(15°) = (√3 - 1)/(√3 + 1)

⇒ tan(15°) = (√3 - 1)²/3 - 1  (multiplying with √3 - 1 in the numerator and denominator)

⇒ tan(15°) = (3 + 1 - 2√3)/2

⇒ tan(15°) = (4 - 2√3)/2

⇒ tan(15°) = (2 - √3)

⇒ tan(13π/12) = tan(π/12) = tan(15°) = (2 - √3)