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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(9090)cos0+cos(9088)cos2+.............+cos(9046)cos(44)+sin(44)sin(9046)+sin(42)sin(9048)+............+sin0 sin(9090)=cos0 cos0+cos2.cos2+............+cos44 cos44+sin44 sin44+..........+sin2.sin2+sin0. sin0=cos20+cos22+............+cos244+sin244+............+sin22+sin201+1+1+.........+1 (23 times)=23


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