Question

prove that tan 1°tan2°tan 3°....tan89° =1
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Answer 1

Answer:

tan1°tan2°tan3°...tan87°tan88°tan89°

tan(90-1)tan(90-2)tan(90-3)...tan87°tan88°tan89°

cot89°cot88°cot87°... tan87°tan88°tan89°

1/tan89°×1/tan88°×1/tan87°...tan87°tan88°tan89°{since cot=1/tan}

Now cut that and the ans will be 1