Question

prove that cot5 cot25 cot45 cot65 cot85=1
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Answer 1

cot5 = tan(90-5) = tan85

cot25 = tan(90-25) = tan65

cot45 = 1

Since tanX × cotX = 1/cotX × cotX = 1

cot5×cot85 = tan85×cot85 = 1

cot25×cot65 = tan65×cot65 = 1

cot45 = 1

Therefore,

cot5×cot25×cot45×cot65×cot85 = 1×1×1 = 1

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Answer 2

cot5.cot25.cot 45. Cot65.cot85=1

Cot (90-85).Cot(90-65).1/Tan45. Cot65.Cot85=1. (Cot=1/tan)

Tan85.Tan65.1/1.Cot65.Cot85=1. (Tan45=1)

1×1×1=1. (.=×)

1=1