If sec A = cosec A and 0° ≤ A ≤ 90°, state the value of A.

sec A = cosec A

$\dfrac{1}{\text{cos A}} = \dfrac{1}{\text{sin A}}$

sin A = cos A

As we know that sin² A + cos² A = 1

⇒ sin² A + sin² A = 1

⇒ 2sin² A = 1

⇒ sin² A = $\dfrac{1}{2}$

⇒ sin A = $\dfrac{1}{\sqrt2}$

⇒ sin A = sin 45°

⇒ A = 45°

Hence, the value of A = 45°.