Question

complete the sentence so the result is an identity. let x be any real number.
\\(\frac{\sin x}{\tan x}=\\)

a. \\(\cot x\\)
b. \\(\csc x\\)
c. \\(\cos x\\)
d. \\(\sec x\\)

Explanation:

Step1: Recall the tangent identity

Recall that $\tan x=\frac{\sin x}{\cos x}$.

Step2: Substitute tangent in the given expression

Substitute $\tan x$ in $\frac{\sin x}{\tan x}$, we get $\frac{\sin x}{\frac{\sin x}{\cos x}}$.

Step3: Simplify the complex - fraction

Using the rule $\frac{a}{\frac{b}{c}}=\frac{a\times c}{b}$, we have $\frac{\sin x\times\cos x}{\sin x}$.

Step4: Cancel out the common terms

Cancel out the $\sin x$ terms. So, $\frac{\sin x\times\cos x}{\sin x}=\cos x$.

Answer:

C. $\cos x$