The first thing you have to realize is that tangent is the slope of a curve on a given point. You can solve for the slope by finding the derivative of the given function. So:
\(\frac{d}{dx} xsin(x)\)
Next use product rule (I recommend watching videos if you're confused):
\(= [sin(x)] + [x*cos(x)]\)
Next substitute you x-value (π/2) into your derivative:
\(= [sin( \frac{ \pi}{2} )] +[ \frac{\pi}{2}*cos( \frac{\pi}{2})]\)
\(= 1 + \frac{\pi}{2} *0\)
\(= 1\)
So our slope at π/2 is 1. Next we use our slope-form and substitute our given value and solve for y-intercept (algebra-stuff)
\(( \frac{\pi}{2}) = 1( \frac{\pi}{2}) + b\)
\(b = 0\)
So we get our equation:
\(y = x\)
So our answer is E
Feel free to ask any questions.
Hopes this helps!
