Question

Albert wants to show that tan θ sin θ + cos θ = sec θ. He writes the following proof:

Answer 1

The answer is the second one ⇒ he should write cosФ = cos²Ф/cosФ to find a common denominator

Explanation:

∵ tanФ = sinФ/cosФ

∴ (sinФ/cosФ) (sinФ) + cosФ

∵ cosФ = cos²Ф/cosФ

∴ (sin²Ф/cosФ) + cosФ = (sin²Ф/cosФ) + (cos²Ф/cosФ)

∴ = (sin²Ф + cos²Ф)/cosФ

∵ sin²Ф + cos²Ф = 1

∴ tanФ sinФ + cosФ = 1/cosФ = secФ