Answer :
Certainly! Let's simplify the given expression step-by-step:
[tex]\[ \frac{\tan x \cos x}{\sin x} \][/tex]
1. Recall the definition of [tex]\(\tan x\)[/tex]. The tangent function is defined as the ratio of the sine of [tex]\(x\)[/tex] to the cosine of [tex]\(x\)[/tex]:
[tex]\[ \tan x = \frac{\sin x}{\cos x} \][/tex]
2. Substitute [tex]\(\tan x\)[/tex] in the original expression:
[tex]\[ \frac{\left( \frac{\sin x}{\cos x} \right) \cos x}{\sin x} \][/tex]
3. Simplify inside the numerator. Notice that [tex]\(\frac{\sin x}{\cos x} \cdot \cos x\)[/tex] simplifies to [tex]\(\sin x\)[/tex]:
[tex]\[ \frac{\sin x}{\sin x} \][/tex]
4. Finally, any non-zero value divided by itself is 1:
[tex]\[ \frac{\sin x}{\sin x} = 1 \][/tex]
Therefore, the simplified form of the expression is:
[tex]\[ 1 \][/tex]
Thus, the result is:
[tex]\[ 1 \][/tex]
[tex]\[ \frac{\tan x \cos x}{\sin x} \][/tex]
1. Recall the definition of [tex]\(\tan x\)[/tex]. The tangent function is defined as the ratio of the sine of [tex]\(x\)[/tex] to the cosine of [tex]\(x\)[/tex]:
[tex]\[ \tan x = \frac{\sin x}{\cos x} \][/tex]
2. Substitute [tex]\(\tan x\)[/tex] in the original expression:
[tex]\[ \frac{\left( \frac{\sin x}{\cos x} \right) \cos x}{\sin x} \][/tex]
3. Simplify inside the numerator. Notice that [tex]\(\frac{\sin x}{\cos x} \cdot \cos x\)[/tex] simplifies to [tex]\(\sin x\)[/tex]:
[tex]\[ \frac{\sin x}{\sin x} \][/tex]
4. Finally, any non-zero value divided by itself is 1:
[tex]\[ \frac{\sin x}{\sin x} = 1 \][/tex]
Therefore, the simplified form of the expression is:
[tex]\[ 1 \][/tex]
Thus, the result is:
[tex]\[ 1 \][/tex]
