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Question

Compute the following:
(i)[abba]+[abba]

(ii)[a2+b2b2+c2a2+c2a2+b2]+[2ab2bc2ac2ab]

(iii)1468516285+1276805324

(iv)[cos2xsin2xsin2xcos2x]+[sin2xcos2xcos2xsin2x]

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Solution

[abba]+[abba]=[a+ab+bb+ba+a]=[2a2b02a]

[a2+b2b2+c2a2+c2a2+b2]+[2ab2bc2ac2ab]=[a2+b2+2abb2+c2+2aba2+c22aca2+b22ab]=[(a+b)2(b+c)2(ac)2(ab)2][(a+b)2=a2+2ab+b2(ab)2=a22ab+b2]

1468516285+1276805324=1+124+76+68+85+1016+52+38+25+4=11110165215109

[cos2xsin2xsin2xcos2x]+[sin2xcos2xcos2xsin2x]=[cos2x+sin2xsin2x+cos2xsin2x+cos2xcos2x+sin2x]=[1111][sin2x+cos2x=1]


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