Question

How do you use the double angle or half angle formulas to find the exact value of `tan2x` given tanx = 7/13, 0 < x < pi/2??

Answer 1

Find tan 2x
Ans: `2366/1560`

Explanation:

tan x = 7/13. Find tan 2x
Apply the trig identity: tan 2x = (2tan x)/(1 - tan^2 x) =
`tan 2x = (2(7/13))/(1 - 49/169) = (14/13)(169/120) = 2366/1560`
Check by calculator.

tan x = 7/13 --> x = 28^@30 --> 2x = 56.60 --> tan 56.60 = 1.51. OK