Question

If tan alpha =cot beta, then find the value of alpha + beta

Answer 1

We have:

tan(A)=cot(B) tanA×tanB = 1 {cot B =1/tan A}

since

tan(A+B) = (tan A + tan B)/(1-tanA

× tanB)

tan(A+B)=(tanA+tanB)/(1-1)

tan(A+B)=not defined

A+B=pi/2 [tan(pi/2)=not

defined]

Answer 2

We have:

tan(A)=cot(B) tanA×tanB = 1 {cot B =1/tan A}

since

tan(A+B) = (tan A + tan B)/(1-tanA

× tanB)

tan(A+B)=(tanA+tanB)/(1-1)

tan(A+B)=not defined

A+B=pi/2 [tan(pi/2)=not

defined]