What is the value of cos 45°?

1/√2 ≈ 0.707

Cos 45° = 1/√2 = √2/2. In a 45-45-90 triangle, both legs are equal, so the ratio of adjacent over hypotenuse is 1/√2.

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

1. Identify which ratio the question needs — sin, cos, tan or a reciprocal.
2. Recall the standard-angle value, or use the right triangle it comes from.
3. Apply identities such as sin²θ + cos²θ = 1 when the angle is not standard.
4. 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.