1.

If \(sin\left( {A - B} \right) = \frac{1}{2}\) and \(\cos \left( {A + B} \right) = \frac{1}{2}\) where A > B > 0 and A + B is an acute angle, then the value of angle B is1). π/62). π/123). π/44). π/2

Answer»

GIVEN,

$(sin\left( {A - B} \right) = \frac{1}{2})$

$(\because\sin \frac{\pi }{6} = \frac{1}{2})$

∴ A – B = π/6…..(1)

And,

$(cos\left( {A + B} \right) = \frac{1}{2})$

$(\because\cos \frac{\pi }{3} = \frac{1}{2})$

∴ A + B = π/3…..(2)

(2) – (1)

A + B – A + B = π/3 – π/6

⇒ 2B = π/6

⇒ B = π/12


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