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Find the EXACT value of sin(A−B)sin(A-B) if sin A = 3/10 and cos B = √13/7. Assume A and B are Quadrant I angles in standard position.

sin(A-B) =

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1 Answer

sin(A-B)=sinAcosB-cosAsinB.

sinA=3/10; cosB=√13/7.

cosA=√(1-sin²A)=√(1-9/100)=√(91/100)=√91/10.

sinB=√(1-cos²B)=√(1-13/49)=6/7.

sin(A-B)=(3/10)√13/7-(√91/10)6/7=3√13/70-6√91/70=

(3√13-6√91)/70=3√13(1-2√7)/70.

by Top Rated User (1.2m points)

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