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In the given figure, ABCD is a rectangle in which AB = 60 and BC = 40 cm . If P, Q, R and S be the mid - points of AD, DC, CB and BA, find the area of the shaded region. |
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Answer» Here are two for the price of one (using Euler's formula):COS(A+B)+isin(A+B)≡ei(A+B)≡eiA×eiB≡[cos(A)+isin(A)][cos(B)+isin(B)]≡[cos(A)cos(B)−SIN(A)sin(B)]+i[sin(A)cos(B)+cos(A)sin(B)]Now EQUATE imaginary parts to GIVE the result for sin(A+B) (and, if you WANT, equate real parts to give the result for cos(A+B)). |
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