verify the identity.\n\\frac{\\csc \\theta \\sin \\theta}{\\cot \\theta}=\\tan \\theta\n\nto verify the…

verify the identity.\n\\frac{\\csc \\theta \\sin \\theta}{\\cot \\theta}=\\tan \\theta\n\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 \n\\frac{\\csc \\theta \\sin \\theta}{\\cot \\theta}=\\frac{\\csc \\theta \\square}{\\cot \\theta}\n=\\frac{\\square}{\\cot \\theta}\n=\\tan \\theta

verify the identity.\n\\frac{\\csc \\theta \\sin \\theta}{\\cot \\theta}=\\tan \\theta\n\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 \n\\frac{\\csc \\theta \\sin \\theta}{\\cot \\theta}=\\frac{\\csc \\theta \\square}{\\cot \\theta}\n=\\frac{\\square}{\\cot \\theta}\n=\\tan \\theta

Answer

Explanation:

Step1: Substitute (\sin\theta)

We know that (\csc\theta=\frac{1}{\sin\theta}), so (\frac{\csc\theta\sin\theta}{\cot\theta}=\frac{\csc\theta\times\sin\theta}{\cot\theta}). Since (\csc\theta\times\sin\theta = 1), the expression becomes (\frac{1}{\cot\theta}).

Step2: Use the reciprocal identity

We know that (\tan\theta=\frac{1}{\cot\theta}).

Answer:

(\frac{\csc\theta\sin\theta}{\cot\theta}=\frac{\csc\theta\times\sin\theta}{\cot\theta}=\frac{1}{\cot\theta}=\tan\theta)