equation of the tangent line to the graph of $$ f(x)=\sin x \cos x $$ passing through the point $$ \left(\frac{3 \pi}{4},-\frac{1}{2}\right. $$ $$ f, a: \mathbb{R} \rightarrow \mathbb{R} $$ that $$ f(x)=(x-2)^{2} g(x) $$ for all $$ x \in \mathbb{R} $$ and that $$ a $$ is NOT differentiable at $$ x=2 $$,

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To find the equation of the tangent line to the graph of $$ f(x) = \sin x \cos x $$ passing through the point $$ \left(\frac{3 \pi}{4}, -\frac{1}{2}\right) $$, we need to follow these steps:

1. Find the derivative of $$ f(x) = \sin x \cos x $$ to get the slope of the tangent line.
2. Use the point-slope form of a line to find the equation of the tangent line.
3. Verify that the tangent line passes through the given point.

Let's start by finding the derivative of $$ f(x) = \sin x \cos x $$.
Evaluate the derivative by following steps:
- step0: Evaluate the derivative:
  $$\frac{d}{dx}\left(\sin\left(x\right)\cos\left(x\right)\right)$$
- step1: Use differentiation rules:
  $$\frac{d}{dx}\left(\sin\left(x\right)\right)\times \cos\left(x\right)+\sin\left(x\right)\times \frac{d}{dx}\left(\cos\left(x\right)\right)$$
- step2: Find the derivative:
  $$\cos\left(x\right)\cos\left(x\right)+\sin\left(x\right)\times \frac{d}{dx}\left(\cos\left(x\right)\right)$$
- step3: Calculate:
  $$\cos^{2}\left(x\right)+\sin\left(x\right)\times \frac{d}{dx}\left(\cos\left(x\right)\right)$$
- step4: Find the derivative:
  $$\cos^{2}\left(x\right)+\sin\left(x\right)\left(-\sin\left(x\right)\right)$$
- step5: Calculate:
  $$\cos^{2}\left(x\right)-\sin\left(x\right)\sin\left(x\right)$$
- step6: Simplify:
  $$\cos^{2}\left(x\right)-\sin^{2}\left(x\right)$$
- step7: Transform the expression:
  $$\cos^{2}\left(x\right)-\left(1-\cos^{2}\left(x\right)\right)$$
- step8: Calculate:
  $$\cos^{2}\left(x\right)-1+\cos^{2}\left(x\right)$$
- step9: Add the terms:
  $$2\cos^{2}\left(x\right)-1$$
- step10: Transform the expression:
  $$2-2\sin^{2}\left(x\right)-1$$
- step11: Subtract the numbers:
  $$1-2\sin^{2}\left(x\right)$$
- step12: Transform the expression:
  $$1-2+2\cos^{2}\left(x\right)$$
- step13: Subtract the numbers:
  $$-1+2\cos^{2}\left(x\right)$$
- step14: Transform the expression:
  $$-1+1+\cos\left(2x\right)$$
- step15: Remove the opposites:
  $$\cos\left(2x\right)$$
The derivative of $$ f(x) = \sin x \cos x $$ is $$ \cos(2x) $$.

Now, we can use the point-slope form of a line to find the equation of the tangent line. The point-slope form is given by:

$$ y - y_1 = m(x - x_1) $$

where $$ (x_1, y_1) $$ is the given point and $$ m $$ is the slope of the tangent line.

Given point: $$ \left(\frac{3 \pi}{4}, -\frac{1}{2}\right) $$

Slope of the tangent line: $$ \cos(2 \cdot \frac{3 \pi}{4}) = \cos(\frac{3 \pi}{2}) = 0 $$

Substitute the values into the point-slope form to find the equation of the tangent line.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{-1}{2}-0\times \left(\frac{3\pi }{4}-\frac{3\pi }{4}\right)$$
- step1: Multiply:
  $$\frac{-1}{2}+0$$
- step2: Rewrite the fraction:
  $$-\frac{1}{2}+0$$
- step3: Remove 0:
  $$-\frac{1}{2}$$
The equation of the tangent line to the graph of $$ f(x) = \sin x \cos x $$ passing through the point $$ \left(\frac{3 \pi}{4}, -\frac{1}{2}\right) $$ is $$ y = -\frac{1}{2} $$.

Therefore, the equation of the tangent line is $$ y = -\frac{1}{2} $$.
The equation of the tangent line to the graph of $$ f(x) = \sin x \cos x $$ passing through the point $$ \left(\frac{3 \pi}{4}, -\frac{1}{2}\right) $$ is $$ y = -\frac{1}{2} $$.

equation of the tangent line to the graph of passing through the point
that for all and that is NOT differentiable at ,

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