Question

If A,B are acute angles, sinA=4/5, tan B=5/12,
cos (A-B)=
​

Answer 1

Step-by-step explanation:

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

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