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If sinA + sinB = a and cosA + cosB= b, then cos(A+B) is equal to____________
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SinA + SinB = a ⇒ 2Sin[(A+B)/2]Cos[(A-B)/2]=a..........................(i) CosA + CosB= b ⇒ 2Cos[(A+B)/2]Cos[(A-B)/2]=b.........................(ii) (i) ÷ (ii) Tan[(A+B)/2]=a/b ⇒ Tan2[(A+B)/2]=(a/b)2 ⇒ Tan2[(A+B)/2]=(a/b)2 Cos(A+B)=[1-Tan2[(A+B)/2]]/[1+Tan2[(A+B)/2]]=[1-(a/b)2]/[1+(a/b)2]=[b2-a2]/[b2+a2] |
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