How do you use the angle sum identity to find the exact value of cos 105?

Litzy Downs

Litzy Downs

Answered question

2022-09-30

How do you use the angle sum identity to find the exact value of cos 105?

Answer & Explanation

Dayana Powers

Dayana Powers

Beginner2022-10-01Added 6 answers

Apply
cos ( a + b ) = cos a cos b sin a sin b
Therefore,
cos 105 = cos ( 60 + 45 )
= cos 60 cos 45 sin 60 sin 45
= ( 1 2 ) × ( 2 2 ) ( 3 2 ) × ( 2 2 )
= 1 4 ( 2 6 )
0.2588
Vrbljanovwu

Vrbljanovwu

Beginner2022-10-02Added 2 answers

using the trigonometric identity
cos ( x + y ) = cos x cos y sin x sin y
cos 105 = cos ( 60 + 45 )
= cos 60 cos 45 sin 60 sin 45
= ( 1 2 × 2 2 ) ( 3 2 × 2 2 )
= 2 4 6 4 = 1 4 ( 2 6 )

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