IIT JEE , AIEEE Forum - Mathematics , Trignometry

Hacker

plz help with this

Q>if cotA1*cotA2*cotA3........cotAn=1

find cosA1*cosA2*cosA3............cosAn

though i've a solution but it is very long plz sugget a shorteer method

arvind1990

is the answer (1/

2)^n!!!

10904him

since cot( ) is 1 or more than 1 thus here it should be exactly one in this case because elsewise the product cannot be 1
Thus A1=A2=A3=...................An=45
cos(45) = 1/ -/ 2
Thus the product = (1/ -/ 2 )^n Ans

pjd_0501

since the product is 1......henceA1.A2.A3....An=1.....therefore,we get only one value which is cos(45)=1/^{[ ]}

2........hence for n such cos ratios...ans is (1/^{[ ]}

2)^n

iitkgp_bipin

Here is the method for objective purpose.

cotA₁cotA₂cotA₃........cotA_n=1

A₁ = A₂ = A₃ =.........=A_n =

/4 satisfies the above equation.

Hence cosA₁ = cosA₂ = cosA₃ =.........=cosA_n = 1/

2

Hence cosA₁cosA₂cosA₃.........cosA_n = (1/

2)ⁿ = 2^-n/2

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