Trigonometry

• Trigonometric ratios
• Trigonometric identities
• Basic trigonometric identities
• Proofs of trigonometric identities based on basic trigonometric identities
• sin²(x) + cos²(x) = 1
• 1 + tan²(θ) = sec²(θ)
• 1 + cot²(θ) = cosec²(θ) 
• tan²θ - [ 1 / cos²θ ] + 1 
• cot²A - cos²A = cot²A cos²A
• 1 + [ tan²A / (1 + sec A) ] = sec A
• (1 + tan²(θ))(1 - sin θ)(1 + sin θ) = 1 
• √ [ (1 + sinθ) / (1 - sinθ) ] = sec θ + tan θ
• sin θ / (1 - cos θ) = cosec θ + cot θ 
• [ sin A / (1 + cos A) ] + [ (1 + cos A) / sin A ] = 2 cosec A
• tan^4(x) + tan^2(x) = sec^4(x) - sec^2(x) 
• [ cos A / (1 - tan A) ] + [ sin A / (1 - cot A)] = sin A + cos A
• [ cos^2A + tan^2A - 1 ] / [ sin^2A ] = [ tan^2A ]
• sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A 
• (1 + cot θ - cosec θ )(1 + tan θ  + sec θ)  = 2