Question

give the newton's method iteration formula needed to compute approximate solution to sin(x)-cos(x)=0

Answer 1

x_0 = [Choose a guess, 0 would be appropriate here]
f(x) = sin(x) - cos(x)
For n = 1, 2, 3, ...
x_n = x_n-1 - f(x_n-1)/f'(x_n-1)
end

Approximate solution would require you to choose a stopping point, which you could probably add yourself, but there's the algorithm.