1
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Question

# sin90∘ cos0∘+sin88∘ cos2∘+sin86∘ cos4∘+..............+sin2∘ cos88∘+sin0∘ cos90∘

A

1

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B

44

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C

22

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D

23

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Solution

## The correct option is D 23 sin90∘ cos0∘+sin88∘ cos2∘+............+sin2∘ cos88∘+sin0∘ cos90∘=cos(90∘−90∘)cos0∘+cos(90∘−88∘)cos2∘+.............+cos(90∘−46∘)cos(44∘)+sin(44∘)sin(90∘−46∘)+sin(42∘)sin(90∘−48∘)+............+sin0∘ sin(90∘−90∘)=cos0∘ cos0∘+cos2∘.cos2∘+............+cos44∘ cos44∘+sin44∘ sin44∘+..........+sin2∘.sin2∘+sin0∘. sin0∘=cos20∘+cos22∘+............+cos2∘44∘+sin244∘+............+sin22∘+sin20∘1+1+1+.........+1 (23 times)=23

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