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Wednesday, April 29, 2015

Prove tan55tan65tan75=tan85 (Method II)

tan55tan65tan75

=tan55tan65tan75tan85tan85

=tan85tan55tan65tan75tan85

=tan85sin55sin65sin75(cos85)cos55cos65cos75sin85

=tan85(sin55sin65)(sin75cos85)(cos55cos65)(cos75sin85)

=tan8512(cos120cos10)12(sin160sin10)12(cos120+cos10)12(sin160+sin10)

=tan85(cos120cos10)(sin160sin10)(cos120+cos10)(sin160+sin10)

=tan8512sin160+12sin10sin160cos10+sin10cos1012sin16012sin10+sin160cos10+sin10cos10

=tan8512sin20+12sin10sin160cos10+12sin2012sin2012sin10+sin160cos10+12sin20

=tan8512sin10sin160cos1012sin10+sin160cos10

=tan85(1)

=tan85 (Q.E.D.)

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