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Mathematics

If sec θ + tan θ + 1 = 0, then sec θ − tan θ is equal to :

  1. −1

  2. 0

  3. 1

  4. 2

Trigonometric Identities

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Answer

⇒ sec θ + tan θ + 1 = 0

⇒ sec θ + tan θ = -1

We know that,

⇒ sec2 θ - tan2 θ = 1

⇒ (sec θ + tan θ)(sec θ - tan θ) = 1

⇒ (-1)(sec θ - tan θ) = 1

⇒ sec θ - tan θ = -1

Hence, option 1 is the correct option.

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