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Popular >

cos(2x)-2sin(x)=1

Solution

cos (2 x) - 2 sin (x) = 1

Solution

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

+1

Solution steps

cos (2 x) - 2 sin (x) = 1

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - 1, sin (x) = 0

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

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

Popular Examples

sqrt(3)cos(x)-sin(x)=-1

3 cos (x) - sin (x) = - 1

solvefor x,g=f(sin(6x-7y))solve for

x, g = f (sin (6 x - 7 y))

arccos((sqrt(3))/2)+arcsin(3x)= pi/2

arccos (\frac{3}{2}) + arcsin (3 x) = \frac{π}{2}

2sin(x)=5cos(x),0<= x<360

2 sin (x) = 5 cos (x), 0^{\circ} \leq x < 36 0^{\circ}

cos(x)=(1-2)/(sqrt(26))

cos (x) = \frac{1 - 2}{26}

Frequently Asked Questions (FAQ)

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