Math Help - Finding the minimum value of a trigonometric expression

|sin x + cos x + tan x + cosec x + sec x + cot x |

I have no idea how to deal with the modulus in this expression.

I think the first thing I would try would be to write the entire function with only sines and cosines. That, I find, sometimes makes things a lot easier to see.

|sin x + cos x + (1/sin x cos x) +( (sin x + cos x)/sin x cos x) |
..then tried to find the minima of the curve after differentiating , but couldn't figure out how to, in the end.

Hmm. You need to be a lot more careful with your parentheses there. What's getting divided by what? Don't write so that people can understand you. Write so that no one can misunderstand you!