Question

If the normal chord drawn at the point \(\left(\frac{15}{2\sqrt{2}}, \frac{15}{2\sqrt{2}}\right)\) to the parabola \(y^2 = 15x\) subtends an angle \(\theta\) at the vertex of the parabola, then \(\sin \frac{\theta}{3} + \cos \frac{2\theta}{3} - \sec \frac{4\theta}{3} =\) ?

• A. 0
• B. 3
• C. 1
• D. 2

Hint:

Use parabola normal properties and trigonometric identities carefully to evaluate the expression.

Answer 1

The Correct Option is B

Using properties of parabola and normal chords, and angle subtended at vertex, the expression evaluates to 3.