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Simplify cos(-195∘) using sum and difference formula?

a) cos(195∘)
b) cos(15∘)
c) cos(165∘) d) cos(345∘)

1 Answer

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The simplification of cos(-195°) is found to be cos(15°), after adding 360° to the given angle and utilizing the cosine symmetry property.

To simplify cos(-195°) using the sum and difference formulas, we can utilize the property that cos(-θ) = cos(θ). Therefore, cos(-195°) is equivalent to cos(195°). However, the given options contain angles that are not exactly 195°. Knowing that cosine is periodic, we can add or subtract a full period (360°) to find an equivalent angle that fits within the range of the given options. By adding 360° to -195°, we get 165°, which is one of the provided options.

The answer in this case is b) cos(15°), as -195° + 360° = 165°, and cos(165°) = cos(180° - 15°) = -cos(15°).

So, by understanding cosine's periodicity and even/odd properties, we can determine that the simplified form of cos(-195°) using the given options is equivalent to b) cos(15°).

User Marcelo Lujan
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