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Question

cotπ20.cot3π20.cot5π20.cot7π20.cot9π20=

A
1
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Solution

The correct option is A 1
cotπ20.cot3π20.cot5π20.cot7π20.cot9π20.cotθ=tanπ2θ
=tanπ2π20.tanπ23π10.cot5π20.cot7π20.cot9π20
=tan9π20.tan7π20.cot5π20.cot7π20.cot9π20
=1cot9π20.1cot7π20.cot5π20.cot7π20.cot9π20
[tanθ=1cotθ]
=cot5π20
cot5×18020 [π=180o]
=cot4Tcot45o
=1

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