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sin²A=1-cos²a
sin (a+b) = sinA.cosB-cosA.sinB
sin (a-b) = sinA.cosB+cosA.sinB
so,,
sin(A+B) sin (A-B)
(sinA.cosB-cosA.sinB) (sinA.cosB+cosA.sinB)
(sinAcosB)² - (cosA.sinB)²
sin²A cos²B - cos²A. sinB²
(1-cos²A) cos²B - cos²A (1-cos²B)
cos²B - cos²A cos²B - cos²A + cos²A cos²B
= cos²B - cos²A.
sin (a+b) = sinA.cosB-cosA.sinB
sin (a-b) = sinA.cosB+cosA.sinB
so,,
sin(A+B) sin (A-B)
(sinA.cosB-cosA.sinB) (sinA.cosB+cosA.sinB)
(sinAcosB)² - (cosA.sinB)²
sin²A cos²B - cos²A. sinB²
(1-cos²A) cos²B - cos²A (1-cos²B)
cos²B - cos²A cos²B - cos²A + cos²A cos²B
= cos²B - cos²A.
AqeelAhmad:
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