Trig Identities Question: sin &#x2061;<!-- ⁡ --> ( 4 t

invioor

invioor

Answered question

2022-07-06

Trig Identities Question: sin ( 4 t ) ( 1 cos ( 2 t ) ) cos ( 2 t ) ( 1 cos ( 4 t ) ) = tan t , 0 < t < π 2 , t π 4 .

Answer & Explanation

Zachery Conway

Zachery Conway

Beginner2022-07-07Added 7 answers

One may write, for appropriate values of t,
sin ( 4 t ) ( 1 cos ( 2 t ) ) cos ( 2 t ) ( 1 cos ( 4 t ) ) = 2 sin ( 2 t ) cos ( 2 t ) ( 1 cos ( 2 t ) ) cos ( 2 t ) ( 1 cos ( 4 t ) ) = 2 sin ( 2 t ) ( 1 cos ( 2 t ) ) ( 1 cos ( 4 t ) ) = 2 sin ( 2 t ) ( 2 sin 2 ( t ) ) ( 2 sin 2 ( 2 t ) ) = 2 sin 2 ( t ) sin ( 2 t ) = 2 sin 2 ( t ) 2 sin ( t ) cos ( t ) = tan ( t )

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