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
The volume of the given pyramid with a squarebase whose side measures 6 inches and the altitude of the pyramid measures 12 inches is 144 cubic inches. The value is obtained by applying the formula for the volume of the pyramid as .
The volume of the pyramid is given by the formula:
Where,
is the area of the base of the pyramid and
h is the height or altitude of the pyramid
As shown in the diagram,
The pyramid has a squarebase whose side measures 6 inches and the altitude of the pyramid is 12 inches
Thus,
Area of the square base,
⇒
⇒ sq. inches
Height of the pyramid h = 12 inches
On substituting the values in the formula,
⇒ × 36 × 12
⇒ 4 × 36
⇒ 144 cubic inches
Therefore, the volume of the given pyramid is 144 cubic inches.
Learn more about the volume of the pyramid here:
#SPJ2
Answer:
144 in³
Step-by-step explanation:
The volume of a pyramid of base area A and height h is
V = (1/3)(A)(h).
Here,
V = (1/3)(6 in)²(12 in) = 144 in³
The required solution is
Given equation is,
Simple linear equation:
Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1.
Now, solving the given equation,
Learn more about the simple linear equation: