DB45
(sin A - sin B)² = sin² A + sin² B - 2 sin A sin B = 9/25 (cosA +cosB)² = cos²A+cos²B + 2 cos A cos B = 16/25 --------------------------------------------------------------------------(+) ..........................1 + 1 + 2(cos A cos B - sin AsinB) = 1 ..........................2 + 2 { cos (A+B)} = 1 ..........................2 . cos (A+B) = 1- 2 = - 1 ..........................cos (A +B) = - 1/2
2) A+B+C = 180 A+B = 180 - c sin (A+B) = sin C = 2/√13 = y/r x ²= r² - y² x² = 13 - 4 = 9 x= 3 tan (A+B) = y/x = 2/3 tan A + tan B / ( 1- tan A tan B ) = tan (A+B) = 2/3 tan A + tan B = (2/3)(1 - 13) = 2/3 (-12) = - 8
(cosA +cosB)² = cos²A+cos²B + 2 cos A cos B = 16/25
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..........................1 + 1 + 2(cos A cos B - sin AsinB) = 1
..........................2 + 2 { cos (A+B)} = 1
..........................2 . cos (A+B) = 1- 2 = - 1
..........................cos (A +B) = - 1/2
sin (A+B) = √(1 - cos²(A+B)) = √(1 - 1/4) = 1/2 √3
2) A+B+C = 180
A+B = 180 - c
sin (A+B) = sin C = 2/√13 = y/r
x ²= r² - y²
x² = 13 - 4 = 9
x= 3
tan (A+B) = y/x = 2/3
tan A + tan B / ( 1- tan A tan B ) = tan (A+B) = 2/3
tan A + tan B = (2/3)(1 - 13) = 2/3 (-12) = - 8