Q.

If  cos(θ1−θ2)cos(θ1+θ2)+cos(θ3+θ4)cos(θ3−θ4)=0  then cotθ1 . cotθ2 . cotθ3 .  cotθ4=

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a

1

b

2

c

–1

d

0

answer is C.

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Detailed Solution

put θ1=1350  θ2=450 ,  θ3=1350  θ4=−450.  Then               cos(θ1−θ2)cos(θ1+θ2)+cos(θ3+θ4)cos(θ3−θ4)=0∴ cotθ1cotθ2cotθ3cotθ4=cot1350cot450cot1350cot(−450)                                          =−1×1×−1×−1 =−1
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