How do you prove [(1)/(1-sinx)]+[(1)/(1+sinx)]=2sec^2x?

The formula can be proven by applying: 1) Least common multiple; 2) applying the trigonometric entity ##sin^2x + cos^2x=1 ##
Head
Key-relation : ##sin^2x + cos^2x=1##
Key-concept: Least common multiple; when no common multiples just multiply the terms in the denominator.
Calculation
The above formula can be proven by transforming left side to right side:
##1/(1-sin x)+1/(1+sin x)= (1+sin x + 1-sin x)/((1+sinx)(1-sinx))##
To arrive to right-hand side just divide the denominator to ##(1+sinx)(1-sinx) ## the least common multiple and multiply the numerator to the remaining since they are all 1 just put the value.
By simple algebra and make use of ##(a-b)(a+b)=a^2 – b^2 ## it can be seen from normal multiplication.
## (1+sin x + 1-sin x)/((1+sinx)(1-sinx))= 2/(1-sin^2x)##
Finally apply: ##sin^2x + cos^2x=1## which gives out ##cos^2x=1 – sin^2x ##
## 2/(1-sin^2x)=2/cos^2x=2*(1/cosx)^2##
To finish remember that ## secx=1/cosx## hence:
## 2*(1/cosx)^2=2sec^2x##