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

The general solution for cos^2(θ)-sin^2(θ)=1 is θ=pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^2(θ)-sin^2(θ)=1

cos^{2} (θ) - sin^{2} (θ) = 1

θ = πn

Degrees

θ = 0^{\circ} + 18 0^{\circ} n

Solution steps

cos^{2} (θ) - sin^{2} (θ) = 1

Rewrite using trig identities

cos^{2} (θ) - sin^{2} (θ)

Use the Double Angle identity:

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

= cos (2 θ)

cos (2 θ) = 1

General solutions for

cos (2 θ) = 1

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 θ = 0 + 2 πn

2 θ = 0 + 2 πn

Solve

2 θ = 0 + 2 πn : θ = πn

2 θ = 0 + 2 πn

0 + 2 πn = 2 πn

2 θ = 2 πn

Divide both sides by

2

2 θ = 2 πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{2 πn}{2}

Simplify

θ = πn

θ = πn

θ = πn

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

cos^{3} (x) = cos^{3} (x) csc (x)

- \frac{1}{2} = sin (θ)

2 sin (2 x) + 3 = 2

csc (θ) = 11

What is the general solution for cos^2(θ)-sin^2(θ)=1 ?
The general solution for cos^2(θ)-sin^2(θ)=1 is θ=pin