If secθ + tanθ = 4, then sec θ – tan θ = ?
0.25
The correct answer is 0.25.
sec²θ − tan²θ = 1 ⇒ (secθ + tanθ)(secθ − tanθ) = 1
4 × (secθ − tanθ) = 1 ⇒ secθ − tanθ = 1/4 = 0.25
Short trick: secθ − tanθ = 1/(secθ + tanθ) = 1/4.
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