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

The general solution for 3cos^2(x)-sin^2(x)-sin^2(x)=0 is x=-0.88607…+pin,x=0.88607…+pin

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

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

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

Solution steps

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

Factor

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

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

Solving each part separately

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

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

3 cos (x) - 2 sin (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

3 sin (a) + cos (a) = 1

4 cos^{2} (x) + 3 = 2 (3 + 1)

2 tan^{2} (x) + cot^{2} (x) - 3 = 0

\frac{( 2 sin ( x ) - 1 )}{( sin ( x ) + 5 )} = 0

sec^{2} (b) = 2 + tan (b)

What is the general solution for 3cos^2(x)-sin^2(x)-sin^2(x)=0 ?
The general solution for 3cos^2(x)-sin^2(x)-sin^2(x)=0 is x=-0.88607…+pin,x=0.88607…+pin