Why does sine squared plus cosine squared equal 1?

cos^2(1 + tan^2) = 1

Derive an identity for cos(2theta), done fast in 56 seconds

PreCalculus - Trigonometry: Trig Identities (31 of 57) Proof cos^2(x)=(1+cos2x)/2

Solve cos^2(θ)=1/4

PreCalculus - Trigonometry: Trig Identities (30 of 57) Proof sin^2(x)=(1-cos2x)/2

sin square theta + cos square theta = 1 How to prove?

(1 - cos^2)(1+ cot^2) = 1

Precalculus 5.1 Using Fundamental Identities

1+cosx=2cos^2(x/2) trigonometry identites solve || 1+cos(theta)

Proof: sin^2 + cos^2 = 1

1 - (sin^2 / (1+cos)) = cos theta

1-cosx = 2sin^2(x/2) trigonometric identites proof || 1-cos theta

A-Level Maths: E5-02 [Trigonometric Identities: Proving sin^2 θ + cos^2 θ = 1]

Q6 | prove that 1 - cos square theta into cosec square theta = 1 | Prove that (1-cos^2⁡θ)cosec^2⁡θ=1

Q77 | Prove that √((1-cos^2⁡θ) sec^2⁡θ)=tan⁡θ | root under 1 - cos square theta sec square theta =

`(sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta`

Sin theta/1+Cos theta + 1+Cos theta / Sin theta = 2 Cosec theta | Mathematics Class 10 | Identity

how to prove 1 + cot^2theta = cosec^2theta | Trigonometric Identities | Class 10 Maths

Convert r^2cos(2theta)=1 to Cartesian