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The number of distinct solutions of sin 5x * cos 3x = sin 9x * cos 7x in [0,π/2] is

The number of distinct solutions of sin 5x * cos 3x = sin 9x * cos 7x in [0,π/2] is

Grade:11

1 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
Dear student

2 sin 5x cos 3x = 2 sin 9x cos 7x
Sin 8x + sin 2x = sin 16x + sin 2x

Sin 8x = 2 sin 8x cos 8x

Cos 8x = 1/2

8x = pi/3
x = pi/24

Regards

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