Answer:
Correct answer: 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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