Solve each of the following on the interval [0, 2):

Question

a) 3 cot²x=1

b) sin x= tan x

Answer 1

a) 3 cot²x = 1

cot²x = 1/3

cot x = √3 /3

x = π/3 , 2π /3

*2π /3≈ 2.094 is extraneous because it's out of the interval:

∴x = π/3

b) sin x= tan x

sin x- tan x = 0

sin x - sin x/ cos x = 0

(cos x• sin x - sin x)/ cos x = 0

[sin x(cos x - 1)] / cos x = 0

tan x (cos x - 1) = 0

tan x = 0 or cos x -1 = 0

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tan x = 0

x = 0

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cos x - 1 =0

cos x = 1

x = 0