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  1. If 4x² – 4x secθ + 1 = 0, then secθ + tanθ = ?
    1. 2x
    2. 1
      2x

    3. 3x
    4. 2x or
      1
      2x
Correct Option: D

4x² – 4x secθ + 1 = 0
= 4x secθ = 4x² + 1

= sec θ =
4x² + 1
4x

∴ tanθ = √sec²θ - 1
= √
(4x² + 1)²
² - 1
4x

= √
16x4 + 88x² + 1 - 16x²
16x²

= ±
4x² - 1
4x

∴ secθ + tanθ
=
4x² + 1
+
4x² - 1
4x4x

=
4x² + 1 + 4x² - 1
=
8x²
4x4x

= 2x
or, secθ + tanθ
=
4x² + 1
-
4x² - 1
4x4x

=
4x² + 1 - 4x² - 1
=
2
=
1
4x4x2x



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