Verifying a Trigonometric Identify: cot(pi/2-x)=tanx I am stuck, I used the difference identity for tan, but tan is undefined at pi/2, so would I just substitute the value for cot pi/2 fir tanA in the tan difference formula? Thanks in advance.

1 Answer
Jul 24, 2018

Please refer to The Explanation.

Explanation:

cot(A-B)=(cotAcotB+1)/(cotB-cotA)cot(AB)=cotAcotB+1cotBcotA.

Letting A=pi/2, B=xA=π2,B=x, we have,

cot(pi/2-x)=(cot(pi/2)cotx+1)/(cotx-cot(pi/2))cot(π2x)=cot(π2)cotx+1cotxcot(π2).

But, cot(pi/2)=0cot(π2)=0.

:. cot(pi/2-x)=(0+1)/(cotx-0)=1/cotx=tanx.

Otherwise, cot(pi/2-x)={cos(pi/2-x)}/{sin(pi/2-x)},

={cos(pi/2)cosx+sin(pi/2)sinx}/{sin(pi/2)cosx-cos(pi/2)sinx},

={(0)(cosx)+(1)(sinx)}/{(1)(cosx)-(0)(sinx)},

=sinx/cosx,

=tanx,