then The Value Of Tan α Tan 2α Tan 3α….tan(2n-1)α Is Equal To

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Question

 then the value of tan α tan 2α tan 3α….tan(2n-1)α is equal to

Solution

Correct option is

1

tan α tan 2α tan 3α….tan(2n-1)α

      = {tan α  tan(2n – 1) α} {tan 2α tan (2n – 2)α}…{tan(n-1)α           tan(n+1)α} tan nα,

      ={tan α tan(π/2- α)} {tan 2α tan(π/2- 2α)}….tan π/4 = 1.1.1…1=1

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