the expression below simplifies to a constant, a single function, or a power of a function. use fundamental…

the expression below simplifies to a constant, a single function, or a power of a function. use fundamental identities to simplify the expression. \n\\frac{\\sin ^{2} x}{\\cos ^{2} x}+\\cot x \\tan x \n\\frac{\\sin ^{2} x}{\\cos ^{2} x}+\\cot x \\tan x=\\square

the expression below simplifies to a constant, a single function, or a power of a function. use fundamental identities to simplify the expression. \n\\frac{\\sin ^{2} x}{\\cos ^{2} x}+\\cot x \\tan x \n\\frac{\\sin ^{2} x}{\\cos ^{2} x}+\\cot x \\tan x=\\square

Answer

Explanation:

Step1: Simplify (\frac{\sin^{2}x}{\cos^{2}x})

Using the identity (\tan x=\frac{\sin x}{\cos x}), so (\frac{\sin^{2}x}{\cos^{2}x}=\tan^{2}x).

Step2: Simplify (\cot x\tan x)

Since (\cot x = \frac{1}{\tan x}), then (\cot x\tan x=\frac{1}{\tan x}\times\tan x = 1).

Step3: Combine the two simplified parts

The original expression (\frac{\sin^{2}x}{\cos^{2}x}+\cot x\tan x) becomes (\tan^{2}x + 1). Using the Pythagorean identity (\tan^{2}x+1=\sec^{2}x).

Answer:

(\sec^{2}x)