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.

Question

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.

Charles Autterson · Accepted Answer

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#,

Abigail Armstrong · Answer

undefined Yes, you can use the difference identity for tangent, but you'll need to handle the issue of cotangent being undefined at π/2. To overcome this, you can rewrite cot(π/2 - x) using the cotangent cofunction identity, which states that cot(π/2 - x) = tan(x). So, cot(π/2 - x) = tan(x). Therefore, the given trigonometric identity is verified.