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Q.

The value of expression 2sin⁡1∘+sin⁡2∘+sin⁡3∘+⋯+sin⁡89∘2cos⁡1∘+cos⁡2∘+⋯+cos⁡44∘+1 is equal to

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a

2

b

12

c

½

d

0

answer is A.

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Detailed Solution

Numerator =2sin⁡1∘+sin⁡89∘+sin⁡2∘+sin⁡88∘+⋯+sin⁡44∘+sin⁡46∘+sin⁡45∘⇒ Numerator   =2sin⁡45∘2cos⁡44∘+cos⁡43∘+⋯+cos⁡1∘+1 NumeratorDenominator=2sin⁡45∘=2
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