Help with Basic Trig Identities?
Can someone show me a full explanation of how:
(xcscx+1)/(xcscx) = (sinx/x)+1
- micatkieLv 71 month agoFavourite answer
The answer is as follows:
- PopeLv 71 month ago
This is not what you wrote, but do you mean this?
[xcsc(x) + 1]/[xcsc(x)] = sin(x)/x + 1
= [xcsc(x) + 1]/[xcsc(x)]
= xcsc(x)/[xcsc(x)] + 1/[xcsc(x)]
= 1 + sin(x)/x
= RHS, for x ≠ kπ for any integer k
It is an identity only subject to the exclusion that I added. It cannot be an identity anywhere csc(x) is undefined, and we can brook no division by zero.