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.

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Answer 1 · 2018-07-24T05:45:17

Please refer to The Explanation.

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

Letting #A=pi/2, B=x#, we have,

#cot(pi/2-x)=(cot(pi/2)cotx+1)/(cotx-cot(pi/2))#.

But, #cot(pi/2)=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#,