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Tan6°*tan42°*tan66°*tan78° = 1

Tan6°*tan42°*tan66°*tan78° = 1

Grade:

2 Answers

Kaustubh Nayyar
27 Points
6 years ago
we know that
tan@*tan(60-@)*tan(60+@) = tan (3@)
just using this we get   tan18 * tan 42 * tan 78 = tan 54 
hence ur given expression becomes
(tan 6 * tan 66 * tan 54) * cot18 = tan 18 * cot18 = 1
Kaustubh Nayyar
27 Points
6 years ago
proof of tan@ * tan (60 – @) * tan (60+@) = tan3@
just change all the expression in terms of sin and cos 
then change the  sin (60 – @) * sin (60+@) /  cos (60 – @) * cos (60+@)   
expression using C&D formulae 
repeat C&D formulae with  the above result and sin@/cos@
you will get the expression as tan3@ in the cubic form

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