differentiating trig ratios

red and white kop!

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find the equation of the tangent to the curve y=cosA + 3sinA at the point where A= pi/2
so i took A=pi/2 to get y= 2sqrt2 and m=sqrt2, with the resulting equation being y=sqrt2(A+2-(pi/2))
apparently that is so wrong, and the answer is y+A=3+(pi/2)
i need help here
 
y-y1=m(x-x1)

(x1,y1)=(A,y(A)) = (pi/2, 3)

m = y'(A) = -sinA+3cosA = -1
 
y = f(A) = cos(A)+3sin(A)\displaystyle y \ = \ f(A) \ = \ cos(A)+3sin(A)

f(A) = sin(A)+3cos(A), f(π/2) = 1 = m\displaystyle f'(A) \ = \ -sin(A)+3cos(A), \ f'(\pi/2) \ = \ -1 \ = \ m

f(π/2) = 3\displaystyle f(\pi/2) \ = \ 3

y3 = 1(Aπ/2), y = A+π/2+3, see graph\displaystyle y-3 \ = \ -1(A-\pi/2), \ y \ = \ -A+\pi/2+3, \ see \ graph

[attachment=0:3iiwzk5y]def.jpg[/attachment:3iiwzk5y]
 

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