(1 - cos²0) sec0 = tan²0
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TO PROVE:
(1 - cos²0) sec0 = tan²0
SOLUTION:
LHS = (1 - cos²θ) secθ
= sin²θ × sec²θ (∵ sinθ = 1 - cos²θ)
= sin²θ × 1/cos²θ (∵ cosθ = 1/secθ)
= (sinθ/cosθ)²
= tan²θ (∵ tanθ = sinθ/cosθ)
RHS = tan²θ
==> LHS = RHS
Hence, Proved ✅
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OTHER TRIGONOMETRIC IDENTITIES
1) cos²A + sin² A = 1
2) cos²A =1 - sin²A
3) sin²A =1 - cos²A
4) sec²A - tan²A = 1
5) 1 + tan²A = sec²A
6) tan²A = sec²A – 1
7) cosec²A - cot²A = 1
8) cot²A + 1 = cosec²A
9) cot²A = cosec²A –1
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