Question

Which trigonometric inequality has no solution over the interval 0<=x<=2 a. csc(x)1>0 b.cos(x)-1>0 c.cot(x)-1>0 d.tan(x)-1>0

Answer 1

Answer:

B

Step-by-step explanation:

a. csc x − 1 > 0

csc x > 1

sin x < 1

x = [0, π/2) U (π/2, 2]

b. cos x − 1 > 0

cos x > 1

x = no solution

c. cot x − 1 > 0

cot x > 1

tan x < 1

x = [0, π/4) U (π/2, 2]

d. tan x − 1 > 0

tan x > 1

x = (π/4, π/2) U (π/2, 3π/4)

Of the 4 options, only B has no solution.