What is the general solution for sin^4(x)=cos^4(x) ?

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

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sin^4(x)=cos^4(x)

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

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

Solution steps

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

Subtract

cos^{4} (x)

from both sides

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

Factor

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

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

Rewrite using trig identities

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

Solving each part separately

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

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

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

Combine all the solutions

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

10. 5^{2} = 6. 7^{2} + 7. 8^{2} - 2 \cdot 6.7 \cdot 7.8 \cdot cos (x)

3 sinh (x) - cosh (x) = 1

tan (4 5^{\circ} + \frac{x}{3}) = 0.58

r = a (1 + sin (x))

cos (2 x) - sin^{2} (x) - 1 = 3 sin (x)

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