Question

Find the range of A = sin²⁰¹⁰θ + cos²⁰¹⁴θ 

Answer 1

Now, 0 < sin²⁰¹⁰θ ≤ sin²θ ....(i)

and 0 < cos²⁰¹⁴θ ≤ cos²θ ....(ii)

Adding (i) and (ii), we get,

0 < sin²⁰¹²θ + cos²⁰¹⁴θ ≤ sin²θ + cos²θ 

⇒ 0 < A ≤ 1

Thus, the range of A = (0, 1]