Question

if tanA.tanB=1, A and B both are acute angle if A=30*, find angle B​

Answer 1

if tanA.tanB equal to 1 and Aand B are acute angle if A equal to 30 so,

anle B =√3

Answer 2

Answer:

as we know,

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

we have given tanA.tanB = 1  .....eq.(2),

by putting eq.(2) in (1),we get

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

we may write,

tan(A+B)/1=tanA + tanB / 0

by cross multiplication,  we get,

tanA + tanB = 0

tanA = - tanB

tanA = tan(-B)

we may also write tan(-B)=tan(180*-B)     {as in second quadrant tan(Q) is negative}

so,  tanA = tan(180-B)

A = 180-B    (.:  A=30*)

from here B = 150*

I hope you will be satisfied by this answer.

Thankyou