Solving Trigonometric Equation

The problem asks for the value of x in degrees, given the equation:

$ \sqrt{2} \sin(5x - 5)^\circ = \tan 45^\circ $

Equation Steps

1. Evaluate Known Tangent Value: We know that $\tan 45^\circ = 1$. Substituting this into the equation gives:

   $ \sqrt{2} \sin(5x - 5)^\circ = 1 $

2. Isolate the Sine Function: Divide both sides by $\sqrt{2}$:

   $ \sin(5x - 5)^\circ = \frac{1}{\sqrt{2}} $

3. Identify the Angle for Sine: Recall that $\sin 45^\circ = \frac{1}{\sqrt{2}}$. Therefore, we can equate the angles:

   $ (5x - 5)^\circ = 45^\circ $

4. Solve for 5x: Add 5 to both sides of the equation:

   $ 5x^\circ = 45^\circ + 5^\circ $

   $ 5x^\circ = 50^\circ $

5. Solve for x: Divide both sides by 5:

   $ x = \frac{50^\circ}{5} $

   $ x = 10 $

The value of x is 10 degrees.