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The value of `tan1^@tan2^@tan3^@...tan89^@` is

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The value of `tan1^@tan2^@tan3^@...tan89^@` is
A. `0`
B. `1`
C. `(1)/(2)`
D. Not defined
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1 Answer

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Correct Answer - B
Given expression, `tan1^(@)tan2^(@)tan3^(@) ... tan89^(@)`
`=tan1^(@)tan2^(@)...tan45^(@)*tan(90^(@)-44^(@))tan(90^(@)-43^(@))...tan(90^(@)-1^(@))`
`=tan1^(@)*cot1^(@)*tan2^(@)*cot2^(@)...tan89^(@)*cot89^(@)`
`1*1...1*1=1`
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