What is the general solution for 4sin^2(x)-6cos^2(x)=0 ?

The general solution for 4sin^2(x)-6cos^2(x)=0 is x=-0.88607…+pin,x=0.88607…+pin

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4sin^2(x)-6cos^2(x)=0

4 sin^{2} (x) - 6 cos^{2} (x) = 0

x = - 0.88607 \dots + πn, x = 0.88607 \dots + πn

Solution steps

4 sin^{2} (x) - 6 cos^{2} (x) = 0

Factor

4 sin^{2} (x) - 6 cos^{2} (x) : 2 (2 sin (x) + 3 cos (x)) (2 sin (x) - 3 cos (x))

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

Solving each part separately

2 sin (x) + 3 cos (x) = 0 or 2 sin (x) - 3 cos (x) = 0

2 sin (x) + 3 cos (x) = 0 : x = arctan (- \frac{3}{2}) + πn

2 sin (x) - 3 cos (x) = 0 : x = arctan (\frac{3}{2}) + πn

Combine all the solutions

x = arctan (- \frac{3}{2}) + πn, x = arctan (\frac{3}{2}) + πn

Show solutions in decimal form

x = - 0.88607 \dots + πn, x = 0.88607 \dots + πn

sin (6 0^{\circ} - a) = 0.598

sin (a) = 0.143

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

sin (a) = 1.25

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

What is the general solution for 4sin^2(x)-6cos^2(x)=0 ?
The general solution for 4sin^2(x)-6cos^2(x)=0 is x=-0.88607…+pin,x=0.88607…+pin