prove that..

Asked by  | 18th Sep, 2008, 08:23: PM

Expert Answer:

we know that tan60o = 3

so we have to prove tan200 tan400tan800=3

write 80 = 60+20 and 40 =60-20

we know tan(A+B) and tan(A-B) .apply them

tan200 tan400tan800 = tan200(3+tan200)(3-tan200) / (1-3tan200)(1+3tan200)

=tan200(3-tan2200) / ( 1-3 tan2200)

=(3tan200-tan3200) / ( 1-3 tan2200)

= tan(3*200 ) = tan600 = 3

hence proved

Answered by  | 20th Sep, 2008, 12:04: AM

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