Question

if A+B=pi/2 then tan A.tanB=​

Answer 1

Answer:

tanA.tanB = 1

Step-by-step explanation:

Given that

A+B = π/2 ------(1)

Tan on both sides for (1) gives

tan ( A + B ) = tan (π/2)

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

so

( tanA + tanB ) / ( 1 - tanA.tanB ) = tan(π/2)

=> ( tanA + tanB ) / ( 1 - tanA.tanB ) = undefined/Infinity

=> ( 1 - tanA.tanB ) = ( tanA + tanB ) / undefined

=> ( 1 - tanA.tanB ) = 0

( since, something/infinity=0 )

=> tanA.tanB = 1

Therefore tanA.tanB = 1

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Answer 2

Answer:

Tan A . Tan B =1 is your answer

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