The value of tan1∘tan2∘tan3∘.....tan89∘ is

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The value of 1^{} 2^{} 3^{}..... 89^{} is

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The value of $tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} ..... tan 8 9^{\circ}$ is

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The value of

tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} ..... tan 8 9^{\circ}

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Given,

tan 1^{0} tan 2^{0} tan 3^{0} ...... tan 8 9^{0}

= tan (9 0^{0} - 1^{0}) tan (9 0^{0} - 2^{0}) tan (9 0^{0} - 3^{0}) ...... tan 8 9^{0}

= cot 8 9^{0} cot 8 8^{0} cot 8 7^{0} ...... tan 8 9^{0}

[

∵ tan (9 0^{0} - θ) = cot θ)

]

= cot 8 9^{0} tan 8 9^{0} cot 8 8^{0} tan 8 8^{0} ...... tan 4 5^{0}

[

b ec a u se tan θ \times cot θ = 1 tan 4 5^{\circ} = 1

]

= 1

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Question Text	The value of $tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} ..... tan 8 9^{\circ}$ is
Answer Type	Text solution:1
Upvotes	150