Question

How do you use the angle sum or difference identity to find the exact value of `cot(pi/2-pi/4)`?

Answer 1

`cot(pi/2-pi/4)=1`

Explanation:

`cot(A-B)=(cotBcotA+1)/(cotB-cotA)`

Hence, `cot(pi/2-pi/4)=(cot(pi/4)cot(pi/2)+1)/(cot(pi/4)-cot(pi/2))`

= `(1×0+1)/(1-0)`

= `(0+1)/(1`

= `1/1=1`