What is the general solution for sin^2(x)-4sin^2(x)+7cos^2(x)=0 ?

The general solution for sin^2(x)-4sin^2(x)+7cos^2(x)=0 is x=-0.99115…+pin,x=0.99115…+pin

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sin^2(x)-4sin^2(x)+7cos^2(x)=0

sin^{2} (x) - 4 sin^{2} (x) + 7 cos^{2} (x) = 0

x = - 0.99115 \dots + πn, x = 0.99115 \dots + πn

Solution steps

sin^{2} (x) - 4 sin^{2} (x) + 7 cos^{2} (x) = 0

Factor

sin^{2} (x) - 4 sin^{2} (x) + 7 cos^{2} (x) : (7 cos (x) + 3 sin (x)) (7 cos (x) - 3 sin (x))

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

Solving each part separately

7 cos (x) + 3 sin (x) = 0 or 7 cos (x) - 3 sin (x) = 0

7 cos (x) + 3 sin (x) = 0 : x = arctan (- \frac{7}{3}) + πn

7 cos (x) - 3 sin (x) = 0 : x = arctan (\frac{7}{3}) + πn

Combine all the solutions

x = arctan (- \frac{7}{3}) + πn, x = arctan (\frac{7}{3}) + πn

Show solutions in decimal form

x = - 0.99115 \dots + πn, x = 0.99115 \dots + πn

(sin (x)) (cos (x)) = 0

sin^{2} (x) - 15 sin (x) cos (x) + 50 cos^{2} (x) = 0

cot (x) = sin^{2} (x)

sec (2 x + 60) = - 1.5

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

What is the general solution for sin^2(x)-4sin^2(x)+7cos^2(x)=0 ?
The general solution for sin^2(x)-4sin^2(x)+7cos^2(x)=0 is x=-0.99115…+pin,x=0.99115…+pin