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:

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