This assignment will assess your skills of solving trigonometric functions and equations. You will explore Compound angles (Sum and difference of angles). Throughout this assignment, we will unravel the mysteries of trigonometric functions, starting with the basics and gradually progressing to more complex problems. We will explore methods for solving trigonometric equations and identities. By the end of this assignment, you will have a solid foundation in trigonometry and the skills necessary to tackle a wide range of mathematical challenges.

You are required to complete all the 4 tasks in this assignment. When you are instructed to make a graph in this assignment, please use . Show all steps and relevant formulae wherever necessary.

**Task 1:**

Before working on this task 1, please read the following reading:

Yoshiwara, K. (2023). .

Reading section 8.1 – will help you understand the concepts more clearly.

Answer the following questions for the given triangle.

- Calculate tan 2θ
- Draw the graphs of tan 2θ and tan θ
- Calculate tan 4θ
- Calculate sin (A+B)
- Calculate cos (θ/2)
- Calculate sin (α/2)

**Task 2:**

Answer the following questions related to the trigonometric equations:

(i) Factorize

(ii) Factorize

(iii) Solve the trigonometric equation if

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**Task 3:**

(i) Find cos A – cos B from the following triangle.

(ii) Express sin A cos C into the sum of trigonometric functions using the following triangle.

**Task 4:**

Write in terms of of the following double angled trigonometric expression:

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