en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

+1

Solution steps

cos (x) + sin^{2} (x) - cos^{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{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

Popular Examples

1-sin(x-(3pi)/2)=-sin(x-pi/2)

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

sin(x+pi/2)=(sqrt(3))/2

sin (x + \frac{π}{2}) = \frac{3}{2}

sqrt(3)tan(2x)=-1

3 tan (2 x) = - 1

2 tan^{2} (3 x) = 6

5cos(x)+1=-2sin^2(x)

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

Frequently Asked Questions (FAQ)

What is the general solution for cos(x)+sin^2(x)-cos^2(x)=0 ?
The general solution for cos(x)+sin^2(x)-cos^2(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=2pin