Q. 94.4( 20 Votes )
If secθ + tanθ = p, then what is the value of secθ – tanθ ?
Given that, sec θ + tan θ = p.
By trigonometric identity, we have
sec2 θ – tan2 θ = 1
So, sec2 θ – tan2 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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