Find the number of solutions of the equation sin 2 </msup> &#x2061;<!-- ⁡ --> 2

Reginald Delacruz

Reginald Delacruz

Answered question

2022-06-22

Find the number of solutions of the equation sin 2 2 x cos 2 8 x = 1 2 cos 10 x lying in the interval ( 0 , π 2 )

Answer & Explanation

scipionhi

scipionhi

Beginner2022-06-23Added 25 answers

sin 2 2 x cos 2 8 x = 1 2 cos 10 x
Use formula
sin 2 α = 1 cos 2 α 2 ; cos 2 α = 1 + cos 2 α 2
1 cos 4 x 2 1 + cos 16 x 2 = 1 2 cos 10 x
2 cos 10 x cos 6 x cos 10 x = 0
cos 10 x = 0 or cos 6 x = 1 2

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