Problem

Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are of $\theta$ only. \[ \sin \theta \sec \theta \cot \theta \] \[ \sin \theta \sec \theta \cot \theta= \]

Solution

Step 1 :Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are of $\theta$ only.

Step 2 :Given expression is $\sin \theta \sec \theta \cot \theta$

Step 3 :The sec function is the reciprocal of the cosine function, and the cot function is the reciprocal of the tangent function, which is the ratio of sine to cosine. So, we can rewrite the expression as follows: $\sin \theta \cdot \frac{1}{\cos \theta} \cdot \frac{\cos \theta}{\sin \theta}$

Step 4 :Simplifying the above expression, we get $\theta = \theta$

Step 5 :Thus, the simplified expression is 1

Step 6 :Final Answer: The simplified expression in terms of sine and cosine is \(\boxed{1}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8445/

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