SOLUTION: Please help me answer this question: Without using a calculator, find the value of tan6° x tan12° x tan18° x ••• x tan84°

Question 1155360: Please help me answer this question:
Without using a calculator, find the value of
tan6° x tan12° x tan18° x ••• x tan84°
Answer by ikleyn(52799) (Show Source): You can put this solution on YOUR website!
.


The key to the solution is this identity  tan(x) = .


It gives


    tan(6°)*tan(84°) = 1

    tan(12°)*tan(78°) = 1

    tan(18)*tan(72°) = 1

    . . . and so on . . . 

    tan(42°)*tan(48°) = 1.



By multiplying all these identities, you will get finally


    tan(6°)*(tan(12°)*tan(18°)* . . . *tan(84°) = 1.


ANSWER.  This product is equal to 1.

Solved.

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