verify that the equation is an identity. \n\\( \\frac{\\cot x}{\\csc x}=\\cos x \\)\nto verify the identity…

verify that the equation is an identity. \n\\( \\frac{\\cot x}{\\csc x}=\\cos x \\)\nto verify the identity, start with the more complicated side and transform it to look like the other side. choose the correct transformations and transform the expression at each step\n\\( \\frac{\\cot x}{\\csc x}=\\frac{\\frac{\\cos x}{\\sin x}}{\\frac{1}{\\sin x}} \\)\nwhat transformation is made in the numerator? apply a quotient identity.\nwhat transformation is made in the denominator? apply a reciprocal identity.\n\\( =\\frac{\\square}{\\square} \\) divide and give the unsimplified numerator and denominator.

verify that the equation is an identity. \n\\( \\frac{\\cot x}{\\csc x}=\\cos x \\)\nto verify the identity, start with the more complicated side and transform it to look like the other side. choose the correct transformations and transform the expression at each step\n\\( \\frac{\\cot x}{\\csc x}=\\frac{\\frac{\\cos x}{\\sin x}}{\\frac{1}{\\sin x}} \\)\nwhat transformation is made in the numerator? apply a quotient identity.\nwhat transformation is made in the denominator? apply a reciprocal identity.\n\\( =\\frac{\\square}{\\square} \\) divide and give the unsimplified numerator and denominator.

Answer

Explanation:

Step1: Simplify the complex fraction

$$ \frac{\frac{\cos x}{\sin x}}{\frac{1}{\sin x}}=\frac{\cos x}{\sin x}\times\frac{\sin x}{1} $$

Step2: Cancel out the common factor

Since (\frac{\cos x}{\sin x}\times\frac{\sin x}{1}), the (\sin x) in the numerator and denominator cancels out. $$ \frac{\cos x}{\sin x}\times\frac{\sin x}{1}=\cos x $$

Answer:

(\cos x)