expand cos(A+B-C) formula
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Step-by-step explanation:
Hello,
Indeed a nice question. Ummm I think we can solve this as cos((a+b)+c). We know cos(x+y) so first let x=a+b and y=c
cos (A + B + C) = cos [(A + B) + C]
= cos (A + B) cos C - sin (A + B) sin C, [applying the formula of cos (α + β)]
= (cos A cos B - sin A sin B) cos C - (sin A cos B + cos A sin B) sin C, [applying the formula of cos (α + β) and sin (α + β)]
= cos A cos B cos C - sin A sin B sin C - sin C sin A cos B - sin B sin C cos A, [applying distributive property]
= cos A cos B cos C (1 - tan A tan B - tan C tan A - tan B tan C)
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