Question

If $\sin A=\sin B$ and $\cos A=\cos B$, then find the value of A in terms of B

• A. $A=2n\pi -B$, $nϵZ$
• B. $A=n\pi +B$, $nϵZ$
• C. $A=n\pi -B$, $nϵZ$
• D. $A=2n\pi +B$, $nϵZ$

Answer 1

The correct option is D $A=2n\pi +B$, $nϵZ$

$\sin A-\sin B=0$ and $\cos A-\cos B=0$

$\Rightarrow$ $2\sin \frac{A-B}{2}\cos \frac{A+B}{2}=0$

and $2\sin \frac{A+B}{2}\cos \frac{B-A}{2}=0$

We observe that the common factor gives $\sin \frac{A-B}{2}=0$.

Thus, $\frac{A-B}{2}=n\pi$, $n\in Z$

$A-B=2n\pi$, $n\in Z$

$A=2n\pi +B$, $n\in Z$