Unit 10 Class 11 Math Notes – Trigonometric Identities (Punjab Board New Book)
Unit 10 (Chapter 10) Class 11 Math Notes – Trigonometric Identities: step-by-step solutions of Exercise 10.1, Exercise 10.2, Exercise 10.3 and Exercise 10.4 for the Punjab Board new book (1st Year). Tap an exercise below to open its PDF solution, then view it online or download it.
This unit is part of our Class 11 maths notes for the Punjab Board new book, where you can open the solutions of the other units.
Exercise Wise Solutions of Unit 10 Class 11 Math
What Each Exercise of Unit 10 Covers
Exercise 10.1 – Angles and Allied Angles
Exercise 10.1 has 6 questions on large and negative angles, allied angles, angles less than \(45^\circ\) and proofs using the angles of a triangle.
Exercise 10.2 – Sum and Difference Identities
Exercise 10.2 has 15 questions on sum and difference identities: exact values such as \(\sin 15^\circ\) and \(\cos 105^\circ\), finding \(\sin(\alpha\pm\beta)\), and writing \(a\sin\theta\pm b\cos\theta\) as \(r\sin(\theta\pm\varphi)\).
Exercise 10.3 – Double, Half and Triple Angle Identities
Exercise 10.3 has 5 questions on double, half and triple angle identities, reducing \(\sin^4\theta\), and finding exact values for \(18^\circ\), \(36^\circ\), \(54^\circ\) and \(72^\circ\).
Exercise 10.4 – Product and Sum Formulae
Exercise 10.4 has 10 questions on converting products to sums and sums to products, for example proving \(\cos20^\circ\cos40^\circ\cos60^\circ\cos80^\circ=\tfrac{1}{16}\).
Key Formulas of Unit 10 Class 11 Math
- \(\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta\)
- \(\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta\)
- \(\sin2\alpha=2\sin\alpha\cos\alpha\), \(\cos2\alpha=1-2\sin^2\alpha\)
- \(\sin3\theta=3\sin\theta-4\sin^3\theta\)
- \(2\sin A\cos B=\sin(A+B)+\sin(A-B)\)
Related Class 11 Math Notes
Continue with Unit 9 Class 11 Math Notes and Unit 11 Class 11 Math Notes, or go back to the Class 11 maths notes hub for all 14 units.
FAQs About Unit 10 Class 11 Math
How many exercises are there in Unit 10?
Unit 10 has four exercises: Exercise 10.1, 10.2, 10.3 and 10.4.
How do I decide the sign when using allied angles?
Find the quadrant of the angle, then use the sign of the original ratio in that quadrant. For example, \(\sin(180^\circ-\theta)=\sin\theta\) but \(\cos(180^\circ-\theta)=-\cos\theta\).
Are these notes for the new book?
Yes. These solutions are for the new Class 11 mathematics book by PECTAA (2025 edition onwards), used by the nine BISE Punjab boards: Lahore, Gujranwala, Faisalabad, Multan, Rawalpindi, Sargodha, Sahiwal, Bahawalpur and Dera Ghazi Khan.