Question 108

If A and B are positive acute angles such that sin (A — B) =1/2 and cos (A+ B) = 1/2 , then A and B are given by

Solution

$$sin (A - B) = \frac{1}{2} = sin 30^{\circ}$$

=> $$A - B = 30^{\circ}$$ ----------Eqn(1)

Again, $$cos (A + B) = \frac{1}{2} = cos 60^{\circ}$$

=> $$A + B = 60^{\circ}$$ ---------Eqn(2)

Adding eqns (1) & (2)

$$2A = 90^{\circ}$$

=> $$A = 45^{\circ}$$ and $$B = 15^{\circ}$$

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