Trigonometry
Trigonometric Equations
csc x cot x + cot x = 0; x [ 0, 2π ]

x=π/2 ,3π/2

Step-by-step explanation:

cot x(csc x+1)=0

either cot x=0

tanx=∞=tan (π/2)

x=π/2

or csc x=-1

or sin x=-1=-sin (π/2)=sin (π+π/2)=sin (3π/2)

x=3π/2

x = π/2, 3π/2

Step-by-step explanation:

cosecxcotx + cotx = 0

cotx(cosecx + 1) = 0

cotx = 0

x = π/2,

π + π/2 = 3π/2

cosecx = -1

x = 3π/2

x = π/2, 3π/2

step- i d k and i d c : )

you: : 0

bye

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240