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Walsh
Mathematics
3 October, 08:10
Prove that
Cos (A+B) + Sin (A-B) = 2sin (45+A). cos (45+B)
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Addisyn Alvarez
3 October, 08:19
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Step-by-step explanation:
cos (A+B) + sin (A-B) = 2 sin (45°+A) cos (45° + B)
= 2 (sin45°cosA + cos45°sinA) (cos45°cosB - sin45°sinB)
But sin45=cos45 = (sqrt2) / 2
= 2 ((sqrt2) / 2 * cosA + (sqrt2) / 2 * sinA) ((sqrt2) / 2 * cosB - (sqrt2) / 2 * sinB)
= 2 ((sqrt2) / 2 * (cosA + sinA)) * ((sqrt2) / 2 * (cosB - sinB))
= 2 * (sqrt2) / 2 * (sqrt2) / 2 * (cosA + sinA) * (cosB - sinB)
= (cosA + sinA) * (cosB - sinB)
= cosAcosB + sinAcosB - cosAsinB - sinAsinB
Regrouping:
= (cosAcosB - sinAsinB) + (sinAcosB - cosAsinB)
= cos (A+B) + sin (A-B)
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