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Question

# Let y=cosx+cos2x+cos3x+cos4x+cos5x+cos6x+cos7xsinx+sin2x+sin3x+sin4x+sin5x+sin6x+sin7x, then which of the following hold good?

A
The value of y when x=π/8 is not defined
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B
The value of y when x=π/16 is 1.
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C
The value of y when x=π/32 is 21 .
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D
The value of y when x=π/48 is 2+3 .
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Solution

## The correct options are B The value of y when x=π/16 is 1. D The value of y when x=π/48 is 2+√3 .sinx+sin2x+sin3x+sin4x+sin5x+sin6x+sin7x=sin7x2sinx2sin4xcosx+cos2x+cos3x+cos4x+cos5x+cos6x+cos7x=sin7x2sinx2cos4x⟹y=cosx+cos2x+cos3x+cos4x+cos5x+cos6x+cos7xsinx+sin2x+sin3x+sin4x+sin5x+sin6x+sin7x=cot4xx=π8⟹y=0x=π16⟹y=cotπ4=1x=π32⟹y=cotπ8=√2+1x=π48⟹y=cotπ12=2+√3

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