Why does sine squared plus cosine squared equal 1?

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Prove that 1+cosx=2cos^2(x/2) and 1-cosx=2sin^2(x/2) trigonometric identites

Integral of (1 - cos 2x)/(1 + cos 2x)

Prove that Sin2x/1-cos2x =cotx | sin2theta/1-cos2theta= cot theta|

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

cos2x/(1 + sin2x) = tan(pi/4 - x) Double and Half Angle Identity

(Method 1) Integral of 1/(1+cos^2(x)) (substitution + substitution)

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

"Visualizing the Identity: Understanding sin⁡2x+cos⁡2x=1\sin^2 x + \cos^2 x = 1,sin2x+cos2x=1

Proof of cos 2x = cos²x - sin²x = 2cos²x - 1 = 1 - 2sin²x = (1 - tan²x) /(1 + tan²x)

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NCERT +1 maths chapter 3 trigonometry cos(3π/2 + x)cos(2π+x)[cot(3π/2-x) + cot(2π+x)]= 1

Prove that :- (1 - cos2x)/(1 + cos2x) = tan²x