Answer:
only (1) and (2) are trigonometric identities.
\(\cot x =\frac{\cos x}{\sin x}\) and \(\tan x =\frac{1}{\cot x}\).
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) \(\cot x =\frac{\cos x}{\sin x}\) is true.
Consider 2) \(\tan x =\frac{1}{\cot x}\) is true.
as \(\tan x\) and \(\cot x\) are inverse of each other.
Consider 3) \(\cosec x =\frac{1}{\cos x}\) is false.
as \(\cosec x\) and \(\sin x\) are inverse of each other.
Thus, correct identity is \(\cosec x =\frac{1}{\sin x}\)
Consider 4) \(\cosec x =\frac{1}{\sec x}\) is false.
as \(\cosec x\) and \(\sin x\) are inverse of each other.
Thus, correct identity is \(\cosec x =\frac{1}{\sin x}\)
Also , \(\sec x =\frac{1}{\cos x}\)
Thus, only (1) and (2) are trigonometric identities.
