What is the value of sin²θ + cos²θ?

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This is the Pythagorean identity. For any angle θ, sin²θ + cos²θ = 1. It derives from the Pythagorean theorem applied to the unit circle.

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.

• Example: If sin θ = 3/5, then cos²θ = 1 − 9/25 = 16/25, so cos θ = 4/5.