Happygirl4694 Happygirl4694
  • 02-08-2022
  • Mathematics
contestada

Rewrite each expression such that the argument x is positive. a. cot(−x)cos(−x) sin(−x)

Respuesta :

LammettHash
LammettHash LammettHash
  • 02-08-2022

[tex]\cos(x)[/tex] is an even function, while [tex]\sin(x)[/tex] is odd. This means

[tex]\cos(-x) = \cos(x) \text{ and } \sin(-x) = -\sin(x)[/tex]

[tex]\cot(x)[/tex] is defined by

[tex]\cot(x) = \dfrac{\cos(x)}{\sin(x)}[/tex]

so it is an odd function, since

[tex]\cot(-x) = \dfrac{\cos(-x)}{\sin(-x)} = \dfrac{\cos(x)}{-\sin(x)} = -\cot(x)[/tex]

Putting everything together, it follows that

[tex]\cot(-x) \cos(-x) \sin(-x) = (-\cot(x)) \cos(x) (-\sin(x)) \\\\~~~~~~~~= \cot(x) \cos(x) \sin(x) \\\\ ~~~~~~~~= \cos^2(x)[/tex]

Answer Link

Otras preguntas

least number that has 2, 3, 4, as factors
A tree was chopped down and cut up in a local forest.The tree changed in shape.What kind of change took place?A.chemical changeB.physical change C.phase changeD
China, Korea, and Japan share cultural similarities in part due to their (1) clashes with Russian imperialists (2) shared river systems (3) contacts through tra
Which of the allies suffered the greatest losses on D-Day
A flight instructor charges $50 per lesson, plus an additional fee for the use of his plane. The charge for the use of the plane varies directly with the square
What is 1997 from 2014????????????
Which of the allies suffered the greatest losses on D-Day
what is the kingdom and phylum of a euglena protest?
Which of the allies suffered the greatest losses on D-Day
Why were people from Africa brought to Georgia?