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Sign of Trigonometric Ratios in Different Quadrants

The number of...

Question

The number of roots of the quadratic equation $8 {sec}^{2} θ - 6 sec θ + 1 = 0$

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Solution

$8 s e c^{2} θ - 6 s e c θ + 1 = 0 L e t s e c θ = t, t h e n 8 t^{2} - 6 t + 1 = 0 8 t^{2} - 4 t - 2 t + 1 = 0 4 t (2 t - 1) - 1 (2 t - 1) = 0 (4 t - 1) (2 t - 1) = 0 ∴ t = 1 / 4 o r 1 / 2 b u t t = s e c θ a n d h e n c e t \geq 1 s o n o s o l u t i o n p o s s i b l e$

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The number of roots of the quadratic equation $8 s e c^{2} θ - 6 s e c θ + 1$ = 0 is

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