Let α, β be such that π

Question

Let α, β be such that π < α − β < 3π. If sin α + sin β = -21/65 and cos α + cos β = -27/65, then the value of cos((α − β)/2) is

Accepted Answer

3/√130. The correct option is derived from the identities for the sum of sines and cosines, which relate to the half-angle formulas. Given the conditions on α and β, the values of sin(α) and sin(β) along with cos(α) and cos(β) allow us to calculate cos((α − β)/2) using the derived relationships, leading to the result of 3/√130.

Let α, β be such that π < α − β < 3π. If sin α + sin β = -21/65 and cos α + cos β = -27/65, then the value of cos((α − β)/2) is

Solution

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