What is the general solution for 8sin^2(x)=8cos^2(x) ?

The general solution for 8sin^2(x)=8cos^2(x) is x=(3pi)/4+pin,x= pi/4+pin

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8sin^2(x)=8cos^2(x)

8 sin^{2} (x) = 8 cos^{2} (x)

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

Solution steps

8 sin^{2} (x) = 8 cos^{2} (x)

Subtract

8 cos^{2} (x)

from both sides

8 sin^{2} (x) - 8 cos^{2} (x) = 0

Factor

8 sin^{2} (x) - 8 cos^{2} (x) : 8 (sin (x) + cos (x)) (sin (x) - cos (x))

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

Solving each part separately

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

sin (x) + cos (x) = 0 : x = \frac{3 π}{4} + πn

sin (x) - cos (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

sin (x) = \frac{6}{8}

tan (x) = 2 + tan (3 x)

2 sin (x) - 3 = 0

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

5 sin (x) = cos (x) - 4

What is the general solution for 8sin^2(x)=8cos^2(x) ?
The general solution for 8sin^2(x)=8cos^2(x) is x=(3pi)/4+pin,x= pi/4+pin