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प्रश्न
If sin α + sin β = a and cos α + cos β = b, then prove that cos(α – β) = `(a^2 + b^2 - 2)/2`
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उत्तर
Consider a2 + b2 = sin2α + sin2β + 2 sin α sin β + cos2α + cos2β + 2 cos α cos β
a2 + b2 = (sin2α + cos2α) + (sin2β + cos2β) + 2[cos α cos β + sin α sin β]
a2 + b2 = 1 + 1 + 2 cos(α – β)
∴ cos(α – β) = `(a^2 + b^2 - 2)/2`
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