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

The general solution for sin^2(2x)-cos^2(2x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}

Degrees

x = 22. 5^{\circ} + 9 0^{\circ} n, x = 67. 5^{\circ} + 9 0^{\circ} n

Solution steps

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

Rewrite using trig identities

sin^{2} (2 x) - cos^{2} (2 x)

Use the Double Angle identity:

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

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

= - cos (2 \cdot 2 x)

- cos (2 \cdot 2 x) = 0

Divide both sides by

- 1

- cos (2 \cdot 2 x) = 0

Divide both sides by

- 1

\frac{- cos ( 2 \cdot 2 x )}{- 1} = \frac{0}{- 1}

Simplify

cos (2 \cdot 2 x) = 0

cos (2 \cdot 2 x) = 0

General solutions for

cos (2 \cdot 2 x) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

Solve

2 \cdot 2 x = \frac{π}{2} + 2 πn : x = \frac{π}{8} + \frac{πn}{2}

2 \cdot 2 x = \frac{π}{2} + 2 πn

Divide both sides by

4

2 \cdot 2 x = \frac{π}{2} + 2 πn

Divide both sides by

4

\frac{2 \cdot 2 x}{4} = \frac{\frac{π}{2}}{4} + \frac{2 πn}{4}

Simplify

\frac{2 \cdot 2 x}{4} = \frac{\frac{π}{2}}{4} + \frac{2 πn}{4}

Simplify

\frac{2 \cdot 2 x}{4} : x

\frac{2 \cdot 2 x}{4}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{π}{2}}{4} + \frac{2 πn}{4} : \frac{π}{8} + \frac{πn}{2}

\frac{\frac{π}{2}}{4} + \frac{2 πn}{4}

\frac{\frac{π}{2}}{4} = \frac{π}{8}

\frac{\frac{π}{2}}{4}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{π}{8}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

Solve

2 \cdot 2 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{8} + \frac{πn}{2}

2 \cdot 2 x = \frac{3 π}{2} + 2 πn

Divide both sides by

4

2 \cdot 2 x = \frac{3 π}{2} + 2 πn

Divide both sides by

4

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

Simplify

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

Simplify

\frac{2 \cdot 2 x}{4} : x

\frac{2 \cdot 2 x}{4}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4} : \frac{3 π}{8} + \frac{πn}{2}

\frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4}

\frac{\frac{3 π}{2}}{4} = \frac{3 π}{8}

\frac{\frac{3 π}{2}}{4}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3 π}{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{3 π}{8}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{3 π}{8} + \frac{πn}{2}

x = \frac{3 π}{8} + \frac{πn}{2}

x = \frac{3 π}{8} + \frac{πn}{2}

x = \frac{3 π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}

Popular Examples

cos^2(x)cos(x)=0

cos^{2} (x) cos (x) = 0

2cos(x)=-3

2 cos (x) = - 3

8sec(x)-3tan^2(x)=7

8 sec (x) - 3 tan^{2} (x) = 7

sin^2(6x)+sin^2(3x)=0

sin^{2} (6 x) + sin^{2} (3 x) = 0

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

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

Frequently Asked Questions (FAQ)

What is the general solution for sin^2(2x)-cos^2(2x)=0 ?
The general solution for sin^2(2x)-cos^2(2x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2