Q. 94.4( 20 Votes )

# If secθ + tanθ = p, then what is the value of secθ – tanθ ?

Answer :

Given that, sec θ + tan θ = p.

By trigonometric identity, we have

sec^{2} θ – tan^{2} θ = 1

So, sec^{2} θ – tan^{2} θ = 1

⇒ (sec θ – tan θ) (sec θ + tan θ) = 1

⇒ sec θ – tan θ = 1/(sec θ + tan θ)

⇒ sec θ – tan θ = 1/p [given]

Hence, sec θ – tan θ = 1/p.

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