If tan x=√5/2, then the possible value of cos x is
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Answer:
4/9
Step-by-step explanation:
As tanx=sinx/cosx=((5)^1/2)/2
2sinx=((5)^1/2)cosx ....1
(sinx)^2 +(cosx)^2 =1 ......2
Put cosx= 2/(5)^1/2 sinx from 1
(Sinx)^2 +(4/5)(sinx)^2=1
By taking lcm and cross multiplying we get
9(sinx)^2 =5
(sinx)^2=5/9
Put in 2
(sinx)^2 + (cosx)^2=1
5/9 + (cosx)^2 =1
1-5/9= (cosx)^2
4/9 = (cosx)^2
cosx=2/3
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