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on 1) oRe T 3R S Itan 20 tan 20 tan 54 tan 55 |
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Answer» tan(π/20) tan(3π/20) tan(5π/20) tan(7π/20) tan(9π/20) = 1. To this end:tan(π/20) tan(3π/20) tan(5π/20) tan(7π/20) tan(9π/20)= tan(π/20) tan(3π/20) tan(5π/20) cot(π/2 - 7π/20) cot(π/2 - 9π/20)via cofunction identity = tan(π/20) tan(3π/20) tan(5π/20) cot(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. |
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