Question

Let sin (A + B) = 1 and sin (A - B) = 1/2, where $A,Bϵ[0,\frac{\pi }{2}]$ .

What is the value of A ?

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{8}$

Answer 1

The correct option is B $\frac{\pi }{3}$

We know that $Sin\left({90}^0\right)=1$ and $Sin\left({30}^0\right)=1/2$

So from the given two equations we get, $A+B={90}^0$ and $A-B={30}^0$

Solving both the equations, we get

$A={60}^o$ and $B={30}^o$

Thus, the value of $A=\frac{\pi }{3}$