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vasorasy8

vasorasy8

Answered question

2022-07-06

Find the value of λ in 3 tan 2 π 7 1 tan 2 π 7 = λ cos π 7

Answer & Explanation

Shawn Castaneda

Shawn Castaneda

Beginner2022-07-07Added 17 answers

Let a = π / 7 then we have
1 + 2 1 tan 2 a = λ cos a
multiplying this with tana we get:
sin a cos 2 a + sin 2 a cos a = λ sin a cos a cos 2 a
so
sin a cos 2 a + sin 2 a cos a = λ sin a cos a cos 2 a
multiplying this with 4 we get
4 sin 3 a = λ sin 4 a
Since sin 3 a = sin 4 a we get λ = 4.

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