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-

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 \dots . i)

\sin (A + B) = \frac{1}{2} = \sin 30

A + B = 30 \dots . . 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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