I am required to taylor expand ln(sec(x)) to obtain the first 3 non-zero terms. What I wanted to know was if anyone knows a quicker method than differentating 6 times (this gets very messy)?
Thanks in advance.
tan(x+pi/4) cos(x + pi/4) = sin(x + pi/4)
tan(x+pi/4) * 0.5 *root(2) (cos(x) - sin(x)) = 0.5 * root(2) (sin(x) + cos(x))
tan(x+pi/4) (cos(x) - sin(x)) = sin(x) + cos(x)
I then let tan(x+pi/4) = a + bx + cx^2 , subbed in the expansions for sin(x) and cos(x) and equated coefficients. Again, can you see an improvement upon this method? Time is very precious in the exam so I'm trying to optimise my working.