This is a tenth unit of the book Mathematics 11 published by Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan. On this page we have provided the solutions of the questions.

After reading this unit the students will be able to

• Define allied angles
• Use fundamental law and its deductions to derive trigonometric ratios of allied angles
• Express $a\sin\theta + b\cos \theta$ in the form $r\sin(\theta +\psi )$ where $a = r\cos\psi$ and $b=r\sin\psi$.
• Derive double angle, half angle and triple angle identities from fundamental law and its deductions.
• Express the product (of sines and cosines) as sums or differences (of sines and cosines)
• Express the sums or differences (of sines and cosines) as products (of sines and cosines)