Prove this standard trigonometric identity: Sin² A=1-cos²A
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To prove:- Sin²A = 1-cos² A
In a right triangle
SinA = P/H
CosA = B/H
substituting the values
(P/H)² = 1- (B/H)²
P²/H² = 1- B²/H²
P²/H² = H² – B²/H². (Taking LCM)
According to P.G.T. H²= P²+ B²
∴H² – B² = P²
∴ P²/H² = P²/ H².
RHS= LSH ( Hence Proved)