Question
Download Solution PDFFind the value of secθ - tanθ, if secθ + tanθ = \(\sqrt5\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
secθ + tanθ = \(\sqrt5\)
Concept used:
sec2θ - tan2θ = 1
Calculation:
sec2θ - tan2θ = 1
⇒ (secθ + tanθ)(secθ - tanθ) = 1
⇒ \(\sqrt5\).(secθ - tanθ) = 1
⇒ secθ - tanθ = \(\frac{1}{\sqrt5}\)
⇒ secθ - tanθ = \(\frac{\sqrt5}{\sqrt5\times\sqrt5}\)
⇒ secθ - tanθ = \(\frac{\sqrt5}{5}\)
∴ The required answer is \(\frac{\sqrt5}{5}\).
Last updated on Jul 8, 2025
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