Question

if A , B are acute angles, sinA=4/5, tanB=5/12 then value of cos(a+b)

Answer 1

$\sf \pmb{Answer :}$

Here ,  You must Note that :

if sin(a) = 4/5, then cos(a) = 3/5 

and if tan(b) =5/12... then sin (b)= 5/13 and cos(b) = 12/13 

{ Because {3,4,5} are pythagorean triples … Similarly, {5,12,13} are also pythagorean triples }

 

Thus ,

sin(a+b) = sin(a).cos(b) + cos(a).sin(b)

             = (4/5).(12/13) + (3/5) . (5/13)

             = (48/65) + (15/65)

             = 63/65

 

Therefore, Answer must be :-  63/65

Answer 2

Answer:

ANSWER IN THE ATTACHMENT.