If cos a = 0.465 and sin b = 0.131 (both angles are acute).

Find the values for:
cos (a+b)=
cos(a-b)=

Please show the steps

Correct  cos (a + b) = 0.345  and cos (a - b) = 0.577

Step-by-step explanation:

If both angles are acute, this means that they belong to the first quadrant in which all trigonometric functions are positive.

We first need to know the basic trigonometric equation or identity:

sin²α + cos²α = 1

given: cos a = 0.465 and sin b = 0.131

we must first calculate sin a and cos b

sin²a = 1 - cos²a ⇒ sin a = √ 1 - cos²a = √1- 0.465² 0 √1 - 0.216 = √0.784

sin a = 0.885

cos²b = 1 - sin²b ⇒  cos b = √1 - sin²b = √1 - 0.131² = √1 -  0.017 = √0.983

cos b = 0.991

cos (a + b) = cos a · cos b - sin a · sin b =  0.465 · 0.991 - 0.885 · 0.131

cos (a + b) = 0.461 - 0.116 = 0.345

cos (a + b) = 0.345

cos (a - b) = cos a · cos b + sin a · sin b =  0.465 · 0.991 + 0.885 · 0.131

cos (a - b) = 0.461 + 0.116 = 0.577

cos (a - b) = 0.577

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