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prove that : $sin(A+B)sin(A-B) = sin^{2}A-sin^{2}B$

written 5.2 years ago by teamques10 ★ 68k

modified 2.6 years ago by pedsangini276 • 4.8k

engineering mathematics

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written 5.2 years ago by teamques10 ★ 68k

Solution:

Sin(A+B)Sin(A-B)

$= (sinAcosB + cosAsinB)(sinAcosB - cosAcosB)$

$=sin^{2}Acos^{2}B - cos^{2}Asin^{2}B$

$=sin^{2}A(1 - sin^{2}B) - (1 - sin^{2}A)sin^{2}B$

$=sin^{2}A - sin^{2}Asin^{2}B - sin^{2}B + sin^{2}Asin^{2}B$

$=sin^{2}A - sin^{2}B$

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