Question

if A=45 degree B=30 degree then verify sin(A-B)= sin A* cos B- cos A*sin B

Answer 1

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$A = 45   \: and \: B = 30 \\ \: Also, \: A – B = 45 – 30 = 15 \\ \therefore \: sin (A - B) = sin 15  \\ = \frac{ \sqrt{6 }- \sqrt{2} }{4} = 0.25881904. \: . \: . \: .(1) \\ \therefore \: sin A cos B - cos A sin B \\ = (sin 45) (cos 30)  - (cos 45) (sin 30) \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} - \frac{1}{ \sqrt{2} } \times \frac{ 1 }{2} \\ = \frac{ \sqrt{3} }{ 2\sqrt{2} } - \frac{1}{2 \sqrt{2} } \\ = \frac{ \sqrt{6 }- \sqrt{2}}{4} \\ = 0.25881904. \: . \: . \: . (2) \\ \therefore \: from \: (1) \: and \: (2) \: \\ sin (A - B) =A cos B - cos A sin B \\ hence \: proved \:$

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