How can I find the exact value of tan(5π/12)?
This question had 2 parts, which the result of the 1st question had to be used.
I need help solving it, and if anyone can explain how its actually done, would be very helpful. This is the last question I need help with for the big assignment I had.
Q: Use the result from the 1st question to find the exact value of tan(5π/12), showing all working out.
The answer for the 1st question was tan (2∝) = 2 tan (∝) / (1 - tan^2)(∝))
Thankyou
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Hello Sarah
tan(5π/6) = 2 tan (5π/12) / (1 - tan² (5π/12)) ...........using given formula
-1/(√3) = 2 tan (5π/12) / (1 - tan² (5π/12)) ............... known fact
(1 - tan² (5π/12)) = -2√3 . tan (5π/12) ........................ clearing denominators
tan² (5π/12)) - 2√3 . tan (5π/12) - 1 = 0 .....................rearranging into a quadratic
tan (5π/12) = [2√3 ± √(12 + 4)] / 2 ....................using quadratic formula
tan (5π/12) = √3 ± 2 ........................................dividing through RHS by 2
tan (5π/12) = √3 + 2 .....................................since 5π/12 is in first quadrant
I hope there is enough working for you to follow this