Question

If tan x = -4/3, then find Cos (x/2)​

Answer 1

tan = 1/cot

cot = cos/sin

Answer 2

Answer:

use identity tan² (x) = 1 + sec2(x)

from here we get the value of sec x =  √1+tan²(x)  ...eq.(1),

put value of tanx = -4/3 in eq (1),

secx = √1+(-4/3)²

here , secx = 5/3

cosx = 1 / secx

so, cosx = 3/5

use another identity cos²(x/2) = 1 + cosx/2  ....eq.(2),

by putting the value of cosx in eq (2),

we get cos²(x/2) = (1+3/5) / 2

                             =4/5

by taking root on both sides,

cos(x/2) = 2/√5