Question

if sin(A+B)= underroot 3 upon 2 and cos(a+4b)=0, then the values of a and b are
a)20 and 40 b)40 and 20 c)50 and 10 d)60 and 0

Answer 1

Answer:

A = 54° , B = 6°

Solution:

Given : sin(A + B) = √3/2 , cos(A + 4B) = 0

To find : A , B = ?

We have ;

=> sin(A + B) = √3/2

=> sin(A + B) = sin60°

=> A + B = 60°

=> A = 60° - B ---------(1)

Also,

=> cos(A + 4B) = 0

=> cos(A + 4B) = cos90°

=> A + 4B = 90°

=> A = 90° - 4B ---------(2)

Now,

From eq-(1) and (2) , we have ;

=> 60° + B = 90° - 4B

=> B + 4B = 90° - 60°

=> 5B = 30°

=> B = 30°/5

=> B = 6°

Now,

Putting B = 6° in eq-(1) , we get ;

=> A = 60° - B

=> A = 60° - 6°

=> A = 54°

Hence,

A = 54° , B = 6°