Trigonometric Equations

We are given that

%5Ctan(A%20%2B%20B)%20%3D%20%5Csqrt%7B3%7D

, which implies:

A%20%2B%20B%20%3D%2060%5E%5Ccirc%20%5Cquad%20%5Ctext%7B(since%20%5C(%20%5Ctan%2060%5E%5Ccirc%20%3D%20%5Csqrt%7B3%7D%20%5C)%20)%7D

Also,

%5Ccos(A%20-%20B)%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D

, which implies:

A%20-%20B%20%3D%2030%5E%5Ccirc%20%5Cquad%20%5Ctext%7B(since%20%5C(%20%5Ccos%2030%5E%5Ccirc%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%5C)%20)%7D

Now, solving the system of equations:

A%20%2B%20B%20%3D%2060%5E%5Ccirc

A%20-%20B%20%3D%2030%5E%5Ccirc

Adding these two equations:

2A%20%3D%2090%5E%5Ccirc%20%5Cquad%20%5CRightarrow%20%5Cquad%20A%20%3D%2045%5E%5Ccirc

Substituting

A%20%3D%2045%5E%5Ccirc

into

A%20%2B%20B%20%3D%2060%5E%5Ccirc

45%5E%5Ccirc%20%2B%20B%20%3D%2060%5E%5Ccirc%20%5Cquad%20%5CRightarrow%20%5Cquad%20B%20%3D%2015%5E%5Ccirc

Therefore, the values of

A

and

B

are

45%5E%5Ccirc

and

15%5E%5Ccirc

Chapter Questions
1 MCQs