Unit 08: Fundamental of Trigonometry

This is a eight unit of the book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. On this page we have provided the solutions of the questions.

After reading this unit the students will be able to

• Use distance formula to establish fundamental law of trigonometry:
  • $\cos(\alpha -\beta)=\cos \alpha \cos\beta+\sin\alpha \sin\beta$,
  • $\cos(\alpha +\beta)=\cos \alpha \cos\beta-\sin\alpha \sin\beta$,
  • $\sin(\alpha \pm \beta)=\sin \alpha \cos\beta \pm \sin\alpha \cos\beta$,
  • $\tan(\alpha \pm \beta)=\dfrac{\tan \alpha \pm \beta}{1 \pm \tan \alpha \tan \beta}$
• Define allied angles and use fundamental law and its deductions to derive trigonometric ratios of allied angles.
• 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).