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7sin 2 x + 3cos 2 x = 4, solve for x.

7sin2x + 3cos2x = 4, solve for x.

Grade:11

2 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
Hello student,
7sin2x + 3cos2x = 4
So, 4sin2x + 3sin2x + 3cos2x = 4
4sin2x + 3 (sin2x + cos2x) = 4
4sin2x + 3(1) = 4
4sin2x = 4 – 3
4sin2x = 1
sin2x = ¼
sin x = ½
So, x = 30 degree.
Kushagra Madhukar
askIITians Faculty 629 Points
one year ago
Dear student,
Please find the solution to your problem below.
 
7sin2x + 3cos2x = 4
So, 4sin2x + 3sin2x + 3cos2x = 4
4sin2x + 3 (sin2x + cos2x) = 4
4sin2x + 3(1) = 4
4sin2x = 4 – 3
4sin2x = 1
sin2x = ¼
Hence, sinx = ½ or – ½
Hence, x = 30o, 150o or 210o, 330o
The general solution can be written as, x = nπ ± π/6
 
Hope it helps.
Thanks and regards,
Kushagra

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