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Question

The value of tan1×tan2×tan3×...×tan89 is :


A

0

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B

1

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C

2

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Solution

The correct options are
A

0


B

1


tanθcotθ=1,

tan(90θ)=cotθ and tan45=1

Given: tan1.tan2,tan3 .......tan88. tan89

=(tan1. tan89),(tan2. tan88).....(tan44.tan46) (tan45)

=[(tan1. tan(901)] . [(tan2. tan(902)]..........[(tan44.tan(9044)].1

=(tan1. cot1). (tan2. cot2) ....... (tan44. cot44)

=1


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