If (√2)cos(A − B) = 1, 2sin(A + B) = (√3) and A, B is a fine angle, then determine A′s and B′s value. Please help me.


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Question Number 125073 by amns last updated on 08/Dec/20

$I f \sqrt{2} c o s (A - B) = 1, 2 s i n (A + B) = \sqrt{3} a n d A, B i s a f i n e$ $a n g l e, t h e n d e t e r m i n e A^{'} s a n d B^{'} s v a l u e .$ $P l e a s e h e l p m e .$
	Answered by som(math1967) last updated on 08/Dec/20

	$\cos (A - B) = \frac{1}{\sqrt{2}} = \cos 45$ $\Rightarrow A - B = 45 . . . . i)$ $\sin (A + B) = \frac{1}{2} = \sin 30$ $A + B = 30 . . . . . ii)$ $i) + ii)$ $2 A = 75$ $A = \frac{75}{2}$ $B = 30 - \frac{75}{2} = - \frac{15}{2}$
	Answered by mr W last updated on 08/Dec/20

	$\cos (A - B) = \frac{1}{\sqrt{2}}$ $\Rightarrow A - B = 2 n π \pm \frac{π}{4}$ $\sin (A + B) = \frac{\sqrt{3}}{2}$ $\Rightarrow A + B = m π + {(- 1)}^{m} \frac{π}{3}$ $\Rightarrow A = \frac{1}{2} [2 n π \pm \frac{π}{4} + m π + {(- 1)}^{m} \frac{π}{3}]$ $\Rightarrow B = \frac{1}{2} [- 2 n π \mp \frac{π}{4} + m π + {(- 1)}^{m} \frac{π}{3}]$
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