Further Engineering Mathematics: Programs and Problems

INFORMATION I. Algebraic Identities 2 2 2 3 3 2 2 3 (a+b) = a +2ab+b (a +b) = a + 3a b + 3ab +b 2 2 2 3 3 2 2 3 (a -b) = a -2ab +b (a -b) = a -3a b + 3ab -b 4 4 3 2 2 3 4 (a + b) = a + 4a b + 6a b + 4ab + b 4 4 3 2 2 3 4 (a -b) = a -4a b + 6a b -4ab + b 2 3 3 2 2 2 a-b = (a -b)(a +b) a -b = (a -b)(a +ab +b) 3 3 2 2 a +b = (a+b)(a -ab+b) II. Trigonometrical Identities 2 2 2 2 (1) sin 0 + cos 0 = 1; sec 0 = 1 + tan 0; 2 2 cosec 0 = 1 + cot 0 (2) sin (A + B) = sin A cos B + cos A sin B sin (A - B) = sin A cos B -cos A sin B cos (A + B) = cos A cos B -sin A sin B cos (A - B) = cos A cos B + sin A sin B tanA+tanB tan(A+B) 1-tanA tanB tanA-tanB tan(A -B) = 1 + tanA tan B (3) Let A = B = 0.