Question

If sec $\theta -cos\theta =3/2(\theta$ is a positive acute angle), then sec $\theta$ is equal to

• A. -1/2
• B. 0
• C. 1/2
• D. 2

Answer 1

Answer: (D)

2

$sec\theta -cos\theta =\frac{3}{2}$
$\frac{1}{cos\theta }-cos\theta =\frac{3}{2}$
Let cos $\theta$ = x
$\frac{1}{x}-x=,\frac{3}{2}$
2(1 - $x^2$) = 3x
2 - $2x^2$ = 3x
$2x^2$ + 3x - 2 = 0
$2x^2$+ 4x - x -2 = 0
2x(x + 2) (x + 2) = 0
(2x - 1)(x + 2) = 0
X = -2, x = $\frac{1}{2}$
cos $\theta$ can never be -2 as its value lies from -1 to 1.
Neglecting (-2)
cos $\theta =\frac{1}{2}$
Hence, sec $\theta$ = 2