Question

if tanA is equals to 3/4 and A+B=90,then find the value of cotB

Answer 1

CotB=Tan(90-B).
Since A+B= 90
Which implies 90-B=A.
Therefore CotB=TanA.
Therefore CotB= 3/4.

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Answer 2

tan=perpendicular/base
thus,
here:
perpendicular=3
base=4
by applying Pythagoras theorem:
3^2 + 4^2= hypotenuse(H)^2
9+16=H^2
25=H^2
H=5..
so sinA=3/5
     cosA=4/5

B=90-A
so,
since sinA=cos(90-A)
  and cosA=sin(90-A)



therefore 3/5=cosB
   and      4/5=sinB


since tanX=sinX/cosX..

tanB=sinB/cosB
tanB=(4/5)/(3/5)
       =4/3

cotB=1/tanB=3/4

so,
cotB=3/4