Answer:
B. 2x + y = pi + 1.
Step-by-step explanation:
y = sin x + 2 cos x
The slope of a line tangent is the derivative, so:
y' = cos x - 2 sin x
At (pi/2, 1) , substituting for x:-
cos pi/2 - 2 sin pi/2
= 0 - 2 * 1 = -2.
So the slope is - 2 and an equation can be found by using the point-slope formula:
y - y1 = m(x - x1) so:
y - 1 = -2(x - pi/2)
y = -2x + pi + 1
2x + y = pi + 1.
