Question

The number of points inside or on the circle x² + y² = 4 satisfying tan⁴ x + cot⁴x + 1 = 3 sin² y, is

• A. One
• B. Two
• C. Four
• D. Infinite

Answer 1

Answer: (C)

Four

Answer 2

tan⁴ x + cot⁴ x + 1 = (tan² x – cot² x)² + 3 і 3

3 sin² y Ј 3

Ю tan⁴ x + cot⁴ x + 1 = 3 sin² y

Ю tan² x = cot² x

& sin² y = 1

Ю tan² x =1

x = ±$\frac{\pi}{4}$, ± $\frac{3\pi}{4}$, .......

and x² Ј 4 Ю x = ±$\frac{\pi}{4}$

sin y = ± 1 Ю y = ±$\frac{\pi}{2}$

Hence four points.