tan⁡81∘−tan⁡63∘−tan⁡27∘+tan⁡9∘ equals

tan81tan63tan27+tan9 equals

  1. A

    6

  2. B

    0

  3. C

    2

  4. D

    4

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    Solution:

    tan81tan63tan27+tan9=tan81+tan9tan63+tan27=sin81cos81+sin9cos9sin63cos63+sin27cos27=sin81cos9+sin9cos81cos9cos81sin63cos27+sin27cos63cos27cos63=sin81+9cos9cos909sin63+27cos27cos9027=sin90cos9sin9sin90cos27sin27=1sin9cos9×221sin27cos27×22=2sin182sin54=2sin54sin18sin18sin54=22cos36sin18sin18cos36=4

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