if cos x= -3/5 & π/2

Question

if cos x= -3/5 & π/2<x<π then find cos x/2, sinx/2 & tanx/2​

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Charlie 3 weeks 2021-11-06T09:05:17+00:00 1 Answer 0 views 0

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    2021-11-06T09:06:43+00:00

    Step-by-step explanation:

    cosx = -3/5

    consider a right angled triangle with base 3, height 4 and hypotenuse 5.

    since cos x is negative and given that x lies in 2nd quadrant, we know that cos x/2 will be positive. Also sin x/2 and tan x/2 will be positive, since x/2 will be in first quadrant

    Now Cos x = -3/5 = 2 cos² x/2 – 1

    cos² x/2 = 1/5

    cos x/2 = +1/√5

    Now sin² x/2 = 1 – cos² x/2 = 4/5

    sin x/2 = +2/√5

    Now tan x/2 = (sin x/2)/(cos x/2) = 2

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