How to prove this trigonometric integral? <mstyle displaystyle="true" scriptlevel="0"> <ms

Tristian Velazquez

Tristian Velazquez

Answered question

2022-06-14

How to prove this trigonometric integral?
π / 4 π / 4 ( cos x sin x cos x + sin x ) cos ( 2 t )   d x = π 2 sin ( π cos 2 t )

Answer & Explanation

Braedon Rivas

Braedon Rivas

Beginner2022-06-15Added 24 answers

cos x sin x cos x + sin x = tan ( π 4 x ) π / 4 π / 4 ( cos x sin x cos x + sin x ) n d x = π / 4 π / 4 tan n ( π 4 x ) d x = 0 π / 2 tan n u d u = π 2 sec n π 2 , 1 < n < 1 = π 2 sec π cos 2 t 2 = π 2 sec π ( 2 cos 2 t 1 ) 2 = π 2 csc ( π cos 2 t )

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