square root of 1+tan^2c

Answer 1

The expression $\sqrt{1+{\tan }^{2}c}$ can be simplified using the Pythagorean identity in trigonometry. According to this identity:

$$1+{\tan }^{2}c={\sec }^{2}c$$

Thus, we can rewrite the square root:

$$\sqrt{1+{\tan }^{2}c}=\sqrt{{\sec }^{2}c}$$

Since the square root of a square gives the absolute value, we have:

$$\sqrt{{\sec }^{2}c}=|\sec c|$$

Therefore, the final result is:

$$\sqrt{1+{\tan }^{2}c}=|\sec c|$$