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

The general solution for cos^2(x)+cos(x)=sin^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = \frac{1}{2}, cos (x) = - 1

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

4 cos (x) + 4 sin (x) tan (x) = 8

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

5 sin (x) tan (x) - 4 tan (x) = 0

5 cos (5 x) = 0

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

What is the general solution for cos^2(x)+cos(x)=sin^2(x) ?
The general solution for cos^2(x)+cos(x)=sin^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin