Prove that sec &#x2061;<!-- ⁡ --> ( 16 A )

Jeramiah Campos

Jeramiah Campos

Answered question

2022-06-24

Prove that sec ( 16 A ) 1 sec ( 8 A ) 1 = tan ( 16 A ) tan ( 4 A )

Answer & Explanation

Harold Cantrell

Harold Cantrell

Beginner2022-06-25Added 21 answers

sec 16 A 1 sec 8 A 1
= 1 cos 16 A 1 1 cos 8 A 1
= 1 cos 16 A cos 16 A 1 cos 8 A cos 8 A
= 2 sin 2 8 A cos 16 A × cos 8 A 2 sin 2 4 A
= 2 sin 8 A cos 8 A cos 16 A × sin 8 A 2 sin 2 4 A
= sin 16 A cos 16 A × 2 sin 4 A cos 4 A 2 sin 2 4 A
= tan 16 A × cos 4 A sin 4 A
= tan 16 A × cot 4 A
= tan 16 A tan 4 A
Makayla Boyd

Makayla Boyd

Beginner2022-06-26Added 6 answers

1 cos 2 ( 16 A ) 1 + cos ( 16 A ) × cos 8 A cos ( 16 A ) × 1 + cos 8 A 1 cos 2 ( 8 A ) = sin 2 16 A 2 cos 2 ( 8 A ) × cos 8 A cos 16 A × 2 cos 2 4 A sin 2 8 A
So
= sin 2 ( 16 A ) sin ( 16 A ) × 2 cos 2 ( 4 A ) cos 16 A × 1 sin ( 8 A ) = tan 16 A tan 4 A

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