Find the value of

To find: Value of $\sec \left(-\frac{25 \pi}{3}\right)$

We have,

$\sec \left(-\frac{25 \pi}{3}\right)=\sec \frac{25 \pi}{3}$

$[\because \sec (-\theta)=\sec \theta]$

Putting π = 180°

$=\sec \frac{25 \times 180}{3}$

$=\sec \left[25 \times 60^{\circ}\right]$

$=\sec \left[1500^{\circ}\right]$

$=\sec \left[90^{\circ} \times 16+60^{\circ}\right]$

Clearly, $1500^{\circ}$ is in Ist Quadrant and the multiple of $90^{\circ}$ is even

$=\sec 60^{\circ}$

$=2\left[\because \sec 60^{\circ}=2\right]$