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for positive acute angles A and B, it is known that cos A= 5/13 and sin B=12/37. find the value of cos (A+B) in simplest form​

Respuesta :

Using trigonometric identity, the value of cos (A + B) in the simplest form is 31 / 481.

How to use trigonometric identity?

Cos(A + B) = Cos A Cos B - Sin A Sin B.

Using trigonometric ratios,

sin B = opposite / hypotenuse

Cos A = adjacent / hypotenuse

cos A = 5 / 13

sin B = 12/37

Using Pythagoras theorem,

13² - 5² = b²

b = √144

b = 12

37² - 12² = a²

a = √ 1225

a = 35

Therefore,

Cos(A + B) = Cos A Cos B - Sin A Sin B.

cos A = 5 / 13

sin A = 12 / 13

sin B = 12 / 37

cos B = 35 / 37

Hence,

Cos(A + B) = 5 / 13 × 35 / 37 - 12 / 13 × 12 / 37

Cos(A + B) =  175 / 481 - 144 / 481

Cos(A + B) =  31 / 481

learn more on trigonometric identity here: https://brainly.com/question/22238860

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