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0.2...600 72- ठ32 |
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Answer» 1. cos(A+B) = cosA cosB - sinA sinB.2. cos(A - B) =cosA cosB + sinA sinB.3. sin(A+B) = sinA cosB +cosA sinB.4. sin(A - B) = sinA cosB - cosA sinB. lets say A+B = C and A-B = DAdd equations of number (1) and (2) , i.e. (1) + (2) ->cos C + cos D = 2 cos [(C+D)/2 ] cos [ (C-D)/2 ]and Subtract equation of number (4) from (3), i.e. (3) - (4) ->sin C - sin D = 2 cos [(C+D) /2 ] sin[(C- D) /2] so cos 7x + cos 5x = 2 cos(12x/2) cos ( 2x/2)and sin 7x - sin 5x = 2 cos(12x/2) sin ( 2x/2 ) (cos 7x + cos 5x)/sin 7x - sin 5x = cos(x)/sin(x)= cot(x). |
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