Why is tan 45° equal to 1?

Because in a right triangle with two 45° angles, the opposite and adjacent sides are equal, so their ratio is 1.

Is tan 45° undefined like tan 90°?

No, tan 45° is defined and equals 1. Tan 90° is undefined because cos 90° = 0.

Trigonometry

What is the value of tan 45°?

Topic: Trigonometry · Difficulty: Easy

All Practice Questions

Quick Summary

Question: What is the value of tan 45°?
Answer: 1

Answer

Step-by-Step Explanation

Tan 45° = sin 45° / cos 45° = (√2/2) / (√2/2) = 1. In a 45-45-90 triangle, both legs are equal, so the tangent ratio is 1.

Understanding Trigonometry questions

Trigonometry connects angles to ratios of side lengths. Most standard-angle questions are solved instantly once the values for 0°, 30°, 45°, 60° and 90° are memorised alongside the three reciprocal ratios.

How to approach it

Identify which ratio the question needs — sin, cos, tan or a reciprocal.
Recall the standard-angle value, or use the right triangle it comes from.
Apply identities such as sin²θ + cos²θ = 1 when the angle is not standard.
Rationalise surds in the final answer where the exam expects it.

Common mistakes to avoid

Confusing sec with cosec, or cot with tan.
Mixing degree and radian mode when checking on a calculator.
Forgetting that tan 90° is undefined rather than zero.

Where it appears: Central to CBSE Class 10–12, IB Mathematics, and JEE/NEET foundation questions.