If sec = √2, then the value of tan =

The given is sec = √2.

The secant of an angle in a right triangle is the hypotenuse divided by the adjacent side.

The tangent of an angle in a right triangle is the opposite side divided by the adjacent side.

Since sec and tan both involve the adjacent side, we can relate them.

The formula to relate sec and tan is: tan = √(sec^2 - 1)

Substitute the given sec value into the formula: tan = √((√2)^2 - 1)

Simplify the equation: tan = √(2 - 1)

So, tan = √1 = 1.