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Amirah Hayden

Amirah Hayden

Answered question

2022-06-02

Prove that cos 20 + cos 100 + cos 140 = 0
Assume A = cos 20 + cos 100 + cos 140 . Prove that value of A is zero.
My try : A = 2 cos 60 cos 40 + cos 140 and I'm stuck here

Answer & Explanation

Redpathdvrgw

Redpathdvrgw

Beginner2022-06-03Added 1 answers

cos 20 + cos 100 = cos ( 60 40 ) + cos ( 60 + 40 ) = cos 40 by using the addition formulae for cos.
Then cos 140 = cos ( 180 40 ) = cos ( 40 ). So
cos 20 + cos 100 + cos 140 = cos 40 cos 40 = 0
virpsojolh8ih

virpsojolh8ih

Beginner2022-06-04Added 1 answers

cos 20 + cos 100 + cos 140 = = cos 20 + cos ( 120 20 ) + cos ( 120 + 20 ) = = cos 20 + cos 120 cos 20 + sin 120 sin 20 + cos 120 cos 20 sin 120 sin 20 = = cos 20 + 2 cos 120 cos 20 = = cos 20 2 cos 60 cos 20 = = cos 20 2 1 2 cos 20 = = cos 20 cos 20 = 0

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