The equation of the tangent line of f(x) is given by y = f'(x)x + c
f(x) = 2sin x
f'(x) = 2cos x
At x = pi/3
f'(pi/3) = 2 cos(pi/3) = 1
f(pi/3) = 2 sin(pi/3) = √3
√3 = 1(π/3) + c
c = √3 - π/3
Therefore, required equation is
y = x + √3 - π/3
The slope of the given line = 1 so the slope of the line perpendicular to it will be -(1/1) = -1.
It also passes through point (1, -1) so we use the point slope equation
y - y1 = m(x - x1)
y - -1) = -1(x - 1)
y + 1 = -x + 1
y = - x <--------- that's the answer
Answer:
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