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if sinA+sinB=a and cosA+cosB=b then cos(A+B)=????

if sinA+sinB=a and cosA+cosB=b
then cos(A+B)=????

Grade:

3 Answers

anish khandelwal
14 Points
10 years ago

solution-B(sq) minus A(sq) by 2

 

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Nanda,

 

Let SinA + SinB = a ------------(1)

and CosA + CosB = b ------------(2)

 

Sq the two eqns, and subtract (2)^2 - (1)^2

You will get, Cos2A+Cos2B+2Cos(A+B) = b2-a2.

So, 2Cos(A+B)Cos(A-B)+2Cos(A+B) = b2-a2.

or Cos(A+B){2Cos(A-B)+2} = b2-a2 ----------------(3)

 

Now Sq the two eqns and add, ie (2)^2+(1)^2

You will get 2+2Cos(A-B) = a2+b2 -----------[Use this in (3)]

 

You'd get Cos(A+B){a2+b2) = (b2-a2).

or Cos(A+B) = (b2-a2)/{a2+b2)

which is the answer.

 

Best Regards,

Ashwin (IIT Madras).

ARPIT NIGAM
15 Points
10 years ago

(sinA + sinB)2=a2  __1      (cosA + Cos B)2 =b2 ___ 2

add 1 & 2 to get value of cos(A-B)

subtract 1 from 2 to get a relation between cos(A+B) & cos(A-B) then substitute value of cos(A-b)

cos(A+B)=b- a2  /  b+ a2

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