If sinx+siny+sinz+sinw=−4, then the value of sin400x+sin300y+sin200z+sin100w is
A
sin400x+sin300y+sin200z+sin100w
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B
sinx+siny+sinz+sinw
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C
4
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D
3
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Solution
The correct option is C4
sinx+siny+sinz+sinw=−4 As −1≤sinθ≤1 Hence sinx=siny=sinz=sinw=−1 Using this we get sin400x+sin300y+sin200z+sin100w=(−1)400+(−1)300+(−1)200+(−1)100=1+1+1+1=4