Answer:
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
Factor the denominator:
(3x-1)(x+2)
every time x=-2 (because of (x+2), it would cause a warp in the graph, and not have an input. that is the vertical asymptote.
since you have factor 3x-1 on top and bottom, in which the zero is 1/3, there would be no solution at x=1/3. it would be a hole.
the answer here is C.
Answer: 51 uinits
The three numbers are x , x + 21 and x + 27.
The greatest of the 3 numbers is x + 27, so x + 27 has to be the hypotenuse.
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Pythagoras Theorem
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a² + b² = c²
x² + (x+21)² = (x+27)²
x² + x² + 42x + 441 = x² + 54x + 729
x² - 12x -288 = 0
(x - 24)(x + 12) = 0
x = 24 or x = -12 (rejected, length cannot be negative)
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Find hypotenuse
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Hypotenuse = x + 27 = 24 + 27 = 51 units
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Answer: 51 units
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