Question

Question #4b672

Answer 1

I couldn't find in trig books any formula of (sec a - sec b).
However, I think we can create one.
Starting from trig identity,
`cos a - cos b = - 2sin ((a+b)/2)sin ((a - b)/2)`
we can write:
`1/(cos a) - 1/(cos b) = (cos b - cos a)/(cos a.cos b)`
`sec a - sec b = [2sin ((a + b)/2).sin ((a - b)/2)]/(cos a.cos b)`
Example: `a = pi/3, and b = pi/4` -->
`(a + b)/2 = (7pi)/24` , and `(a - b)/2 = pi/24`, and
`cos a.cos b = (sqrt2/2)(1/2) = sqrt2/4`.
Finally, we get:
`sec (pi/3) - sec(pi/4) = 2[sin ((7pi)/24).sin (pi/24)]/(sqrt2/4)`