Explanation: The reciprocal identities csc θ = 1 sin θ sec θ = 1 cos θ cot θ = 1 tan θ The quotient identities: tan θ = sin θ cos θ cot θ = cos θ sin θ Applying all these identities, on both sides, we get: 1 sin x + 1 cos x sin x + cos x = cos x sin x + sin x cos x cos x + sin x cos x sin x sin x + cos x = cos x sin x + sin x cos x 1 sin x + cos x × cos x + sin x cos x sin x = cos x sin x + sin x cos x 1 cos x sin x = cos 2 x + sin 2 x sin x cos x Applying the pythagorean identity sin 2 x + cos 2 x = 1 on the right side, we get: 1 cos x sin x = 1 sin x cos x
Applying the pythagorean identity sin 2 x + cos 2 x = 1 on the right side, we get: 1 cos x sin x = 1 sin x cos x
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