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:
[tex] \frac{d}{dx} xsin(x)[/tex]
Next use product rule (I recommend watching videos if you're confused):
[tex]= [sin(x)] + [x*cos(x)][/tex]
Next substitute you x-value (π/2) into your derivative:
[tex]= [sin( \frac{ \pi}{2} )] +[ \frac{\pi}{2}*cos( \frac{\pi}{2})] [/tex]
[tex]= 1 + \frac{\pi}{2} *0[/tex]
[tex]= 1[/tex]
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)
[tex]( \frac{\pi}{2}) = 1( \frac{\pi}{2}) + b [/tex]
[tex]b = 0[/tex]
So we get our equation:
[tex]y = x[/tex]
So our answer is E
Feel free to ask any questions.
Hopes this helps!
