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

Shobhit Singhal , 10 Years ago
Grade 11
anser 2 Answers
Latika Leekha

Last Activity: 10 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

Last Activity: 5 Years 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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