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Question

The value of the expression 2(sin1+sin2+sin3+...+sin89)2(cos1+cos2+...+cos44)+1 is

A
2
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B
12
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C
12
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D
1
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Solution

The correct option is B 2
k=2(sin1+sin2+sin3+....+sin89)2(cos1+cos2+.....+cos44)+1
k=2cos45(sin(9089)+sin(9088)+sin(9087)+.....+sin(9089))(2cos1cos45)+(2cos2cos45)+....+(2cos44cos45)+cos45
We know that 2cosAcosB=cos(A+B)+cos(AB)
k=2(cos1+cos2+cos3+.....+cos89)(cos46+cos44)+(cos47+cos43)+....+(cos89+cos1)+cos45k=2(cos1+cos2+cos3+.....+cos89)(cos1+cos2+cos3+.....+cos89)
k=2(cos1+cos2+cos3+.....+cos89)(cos1+cos2+cos3+.....+cos89)
k=2
Ans: A

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