If sin (A - B) = \frac{1}{2} and cos (A + B) = \frac{1}{2} where A > B > 0 and A + B is an acute angle, then the value B is

Question 5

If sin (A - B) = $$\frac{1}{2}$$ and cos (A + B) = $$\frac{1}{2}$$ where A > B > 0 and A + B is an acute angle, then the value B is

Solution

sin(A-B) = 1/2 $$\Rightarrow$$ A-B = $$\frac{\pi}{6}$$ -------(1)

cos(A+B) = 1/2 $$\Rightarrow$$ A+B = $$\frac{\pi}{3}$$ -------(2)

on solving (1) & (2)

A = $$\frac{\pi}{4}$$

B = $$\frac{\pi}{12}$$

so the answer is option C.

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