18 Find cos sin and tan from the given information Give an e

18. Find cos*. sin-, and tan- from the given information. Give an exact answer 21 tan x = _ 20 and 180°

Solution

180<x<270 => 90 < x/2 < 270

cos(x/2) and tan(x/2) will be negative and sin(x/2) will be positive value

now tan(x) = 2tan(x/2)/(1 - tan²(x/2))

21(1 - tan²(x/2)) = 40tan(x/2)

=> 21tan²(x/2) + 40tan(x/2) - 21 = 0

=> tan(x/2) = -2.333

now sin(x/2) = 2.333/sqrt(2.333² + 1) = 0.9191

cos(x/2) = sin(x/2)/tan(x/2) = -0.3939