Question

Which of the following equations are identities?

cot x = cosx/sinx
tanx = 1/cot x
cscx = 1/cos x
cscx = 1/sec x

Answer 1

only (1) and (2) are trigonometric identities.

`\cot x =(\cos x)/(\sin x)` and
`\tan x =(1)/(\cot x)`.

Explanation:

Given Some trigonometric relations,

We have to check which of the given options are trigonometric identity.

we check one by one,

Consider 1)
`\cot x =(\cos x)/(\sin x)` is true.

Consider 2)
`\tan x =(1)/(\cot x)` is true.

as
`\tan x` and
`\cot x` are inverse of each other.

Consider 3)
`\cosec x =(1)/(\cos x)` is false.

as
`\cosec x` and
`\sin x` are inverse of each other.

Thus, correct identity is
`\cosec x =(1)/(\sin x)`

Consider 4)
`\cosec x =(1)/(\sec x)` is false.

as
`\cosec x` and
`\sin x` are inverse of each other.

Thus, correct identity is
`\cosec x =(1)/(\sin x)`

Also ,
`\sec x =(1)/(\cos x)`

Thus, only (1) and (2) are trigonometric identities.

Answer 2

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.