Question

Find the least value of sinX+cosX+tanX+cosecX+secX+cotX for X belongs to real number.

Answer 1

Step-by-step explanation:

Let sinx+cosx=2–√sin(x+π4)=a, then a can take any value between −2–√ and 2–√. We have sinxcosx=a2−12. Thus

||sinx+cosx+tanx+cotx+secx+cscx|=∣∣∣sinx+cosx+1sinxcosx+sinx+cosxsinxcosx∣∣∣=∣∣∣a+2+2aa2−1∣∣∣=∣∣∣a+2a−1∣∣∣