If 8 cos 2 θ - 2 cos θ - 3 = 0, 0° < θ < 90° , then what is the value of 3 tan θ + cosec θ + cot θ ?
2 \(\sqrt 7 \)
The correct answer is 2 \sqrt 7 .
Secant (\sec\theta) is the reciprocal of cosine, i.e., 1/\cos\theta. Cotangent (\cot\theta) is the reciprocal of tangent, i.e., 1/\tan\theta. It is also \cos\theta / \sin\theta. These definitions and identities are fundamental for solving trigonometric problems like the one discussed above.
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