Question

If $\sin (A-B)=1,2\cos (A+B)=1$ and $0<A+B<{90}^o$, If $A>B$, then the values of $A$ and $B$ are -

• A. $A={45}^o,B={15}^o$
• B. $A={60}^o,B={30}^o$
• C. $A=0^o,B={30}^o$
• D. $A={30}^o,B=0^o$

Answer 1

Answer: (A)

$A={45}^o,B={15}^o$

$\sin (A+B)=\frac{\sqrt{3}}{2}$

$\sin (A+B)=\sin {60}^o$

$A+B={60}^o......\left(1\right)$

$\cos (A-B)=\frac{\sqrt{3}}{2}$

$\cos (A-B)=\cos {30}^o$

$A-B={30}^o......\left(2\right)$

Solving (1) and (2)

$A={45}^o,B={15}^o$