What is the general solution for 7sin^2(x)+2sin^2(x)-3cos^2(x)=0 ?

The general solution for 7sin^2(x)+2sin^2(x)-3cos^2(x)=0 is x=(5pi)/6+pin,x= pi/6+pin

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7sin^2(x)+2sin^2(x)-3cos^2(x)=0

7 sin^{2} (x) + 2 sin^{2} (x) - 3 cos^{2} (x) = 0

x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

Solution steps

7 sin^{2} (x) + 2 sin^{2} (x) - 3 cos^{2} (x) = 0

Factor

7 sin^{2} (x) + 2 sin^{2} (x) - 3 cos^{2} (x) : 3 (3 sin (x) + cos (x)) (3 sin (x) - cos (x))

3 (3 sin (x) + cos (x)) (3 sin (x) - cos (x)) = 0

Solving each part separately

3 sin (x) + cos (x) = 0 or 3 sin (x) - cos (x) = 0

3 sin (x) + cos (x) = 0 : x = \frac{5 π}{6} + πn

3 sin (x) - cos (x) = 0 : x = \frac{π}{6} + πn

Combine all the solutions

x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

sin^{2} (x) - cos^{2} (x) = cos^{4} (x)

sin^{2} (x) + 2 cos^{2} (x) = 1

\frac{sin ^{2} ( a ) + 1}{tan ^{2} ( a )} = 1

2 cos^{2} (x) = - 3 sin (x) cos (x)

4 cos^{2} (x) = sin^{2} (x) + 3

What is the general solution for 7sin^2(x)+2sin^2(x)-3cos^2(x)=0 ?
The general solution for 7sin^2(x)+2sin^2(x)-3cos^2(x)=0 is x=(5pi)/6+pin,x= pi/6+pin