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.
The only inequality that does not have a solution with the range is option B; cos x − 1 > 0.
Inequality is defined as the relation which makes a non-equal comparison between two given functions.
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)
Therefore option B is the only inequality that does not have a solution with the range.
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