tan 45°
1
The value of tan 45° is 1.
This can be derived from the fact that tangent is the ratio of the opposite side to the adjacent side of a right-angled triangle.
Since in a 45-45-90 triangle (an isosceles right triangle), the two legs (opposite sides of the two 45° angles) are congruent, the opposite and adjacent sides are equal in length. Thus, the ratio of opposite to adjacent (tan 45°) is 1.
Alternatively, we can also use the fact that tan 45° is equal to sin 45° divided by cos 45°. Since sin 45° and cos 45° are both equal to root 2 / 2, their ratio is 1, giving us the same result: tan 45° equals 1.
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