Question

Evaluate tan π\20×tan3π\20×tan5π\20×tan7π\20×tan9π\20


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Answer 1

tan(π/20) tan(3π/20) tan(5π/20) tan(7π/20) tan(9π/20)

=tan(π/20) tan(3π/20) tan(5π/20) сot(π/2 - 7/20) сot(π/2 - 9π/20)

=tan(π/20) tan(3π/20) tan(5π/20) сot(3π/20) cot(π/20)

=tan(π/20) tan(3π/20) tan(5π/20) * 1/tan(3π/20) * 1/tan(π/20)

=tan(5π/20)

=tan(π/4)

= 1.

Hope this helps!!

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