Trigonometric identity
- CBSE · NCERT Class 10, Ch 8 Introduction to Trigonometry
A trigonometric identity is an equation in trigonometric ratios that holds for every angle where both sides are defined, such as sin² A + cos² A = 1.
An ordinary equation is true for one or two values. An identity is true for all of them. Class 10 uses three identities. All three come from Pythagoras applied to a right triangle.
- sin² A + cos² A = 1.
- sec² A = 1 + tan² A, for 0° ≤ A < 90°.
- cosec² A = 1 + cot² A, for 0° < A ≤ 90°.
A small example
Say sin A = 3/5 for a sharp angle A. The first identity gives cos² A = 1 − 9/25 = 16/25. So cos A = 4/5. Then tan A = sin A ÷ cos A = 3/4. One ratio has given you all the others.
Where marks go
Question 23 of CBSE's 2026-27 Maths Standard sample paper gives tan θ = 1/√5 and asks for a value built from sec² θ and cosec² θ. In the 2026-27 Maths Standard marking scheme, finding sec² θ with an identity earns half a mark. Finding cosec² θ earns another half. The final value earns 1 mark.
Question 31(A) shows a student's working with an error in it. The scheme gives 1 of the 3 marks just for naming the step where it went wrong. The rest is for the corrected working. This is step marking: each written line can earn its own share.
Sources
Facts last checked against these sources on 30 September 2026.
- NCERT Mathematics, Class X, Chapter 8: Introduction to Trigonometry (reprint 2026-27) · NCERT
- Mathematics Standard (041) Marking Scheme, Class X 2026-27 - Questions 23 and 31(A) · CBSE Academic Unit
- Mathematics Standard (041) Sample Question Paper, Class X 2026-27 - Questions 23 and 31(A) · CBSE Academic Unit
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