Equations cot x = cosx/sinx and tanx = 1/cot x are identities. The correct answers between all the choices given are the first and second choice. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.
Answer:
only (1) and (2) are trigonometric identities.
[tex]\cot x =\frac{\cos x}{\sin x}[/tex] and [tex]\tan x =\frac{1}{\cot x}[/tex].
Step-by-step explanation:
Given Some trigonometric relations,
We have to check which of the given options are trigonometric identity.
we check one by one,
Consider 1) [tex]\cot x =\frac{\cos x}{\sin x}[/tex] is true.
Consider 2) [tex]\tan x =\frac{1}{\cot x}[/tex] is true.
as [tex]\tan x[/tex] and [tex]\cot x[/tex] are inverse of each other.
Consider 3) [tex]\cosec x =\frac{1}{\cos x}[/tex] is false.
as [tex]\cosec x[/tex] and [tex]\sin x[/tex] are inverse of each other.
Thus, correct identity is [tex]\cosec x =\frac{1}{\sin x}[/tex]
Consider 4) [tex]\cosec x =\frac{1}{\sec x}[/tex] is false.
as [tex]\cosec x[/tex] and [tex]\sin x[/tex] are inverse of each other.
Thus, correct identity is [tex]\cosec x =\frac{1}{\sin x}[/tex]
Also , [tex]\sec x =\frac{1}{\cos x}[/tex]
Thus, only (1) and (2) are trigonometric identities.
