Answer :

Given: sec θ + tan θ = x ……………(i)

To find: sec θ – tan θ


We know that 1 + tan2 θ = sec2 θ


1 = sec2 θ – tan2 θ


Now, a2 – b2 = (a – b) (a + b)


1 = sec2 θ – tan2 θ = (sec θ – tan θ) (sec θ + tan θ)


From (i), we have


1 = (sec θ – tan θ) x



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