What is the general solution for cos(x)-2sin^2(x)+1=0 ?

The general solution for cos(x)-2sin^2(x)+1=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

Popular >

cos(x)-2sin^2(x)+1=0

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

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

Solution steps

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

3 tan (2 x) + 3 = 0, 0 \leq x < 2 π

sin (2 x) - sin (x) cos (x) = cos (x)

cot^{2} (x) = 1 - csc (x)

2 sin^{2} (θ) + 9 sin (θ) - 5 = 0

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

What is the general solution for cos(x)-2sin^2(x)+1=0 ?
The general solution for cos(x)-2sin^2(x)+1=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin