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Mathematics
Tamara Thompson
30 March, 02:05
Cot^2x csc^2x + 2 csc^2x - cot^2 = 2
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Aimee Bauer
30 March, 02:54
0
x = π/2 + πk
Step-by-step explanation:
cot² x csc² x + 2 csc² x - cot² x = 2
Multiply both sides by sin² x:
cot² x + 2 - cos² x = 2 sin² x
Add cos² x to both sides:
cot² x + 2 = 2 sin² x + cos² x
Pythagorean identity:
cot² x + 2 = sin² x + 1
Subtract 1 from both sides:
cot² x + 1 = sin² x
Pythagorean identity:
csc² x = sin² x
Multiply both sides by sin² x:
1 = sin⁴ x
Take the fourth root:
sin x = ±1
Solve for x:
x = π/2 + 2πk, 3π/2 + 2πk
Which simplifies to:
x = π/2 + πk
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