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If cos(B-A) =3/5 and tan A=2cotB then cos(A+B)=?pl get me the sol

If cos(B-A) =3/5 and tan A=2cotB then cos(A+B)=?pl get me the sol

Grade:11

1 Answers

Dhairya Shah
11 Points
4 years ago
Given 
COS (B-A) = 3/5 ___(1)
 TAN A=2COT B
 So  sinA/cos A = 2 cos B/ sin A
 So sinAsinB =2cosAcosB____(2)
 
We know that cos B-A =cosBcosA + sinBsinA=3/5     from 1
So 3cosAcosB =3/5   from 2
 On solving we get cosAcosB= 1/5___(3)
    SinAsinB=2/5___(4)
             
Cos (A+B) = cosAcosB – sinAsinB
                  = 1/5 – 2/5     from equations 3 and 4
                  =-1/5

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