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

The general solution for cos^3(x)-sin^2(x)=0 is x=0.71532…+2pin,x=2pi-0.71532…+2pin

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

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

x = 0.71532 \dots + 2 πn, x = 2 π - 0.71532 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

cos (x) \approx 0.75487 \dots

cos (x) = 0.75487 \dots : x = arccos (0.75487 \dots) + 2 πn, x = 2 π - arccos (0.75487 \dots) + 2 πn

Combine all the solutions

x = arccos (0.75487 \dots) + 2 πn, x = 2 π - arccos (0.75487 \dots) + 2 πn

Show solutions in decimal form

x = 0.71532 \dots + 2 πn, x = 2 π - 0.71532 \dots + 2 πn

cos (c) = 0.87

8 sin^{2} (x) - 2 sin (x) - 1 = 0

sin (\frac{1}{4} x) = 0

4 cos^{2} (x) - 4 cos (x) = - 1

2 sec (x) tan (x) = 0

What is the general solution for cos^3(x)-sin^2(x)=0 ?
The general solution for cos^3(x)-sin^2(x)=0 is x=0.71532…+2pin,x=2pi-0.71532…+2pin