Steps to Solve

1. Identify Key Trigonometric Functions

   Review the sine ($\sin$), cosine ($\cos$), tangent ($\tan$) functions and their properties as provided in the image.

2. Understand the Addition Formulas

   The image contains addition formulas, which are fundamental in simplifying trigonometric expressions. For instance:

   • For sine: $$ \sin(A + B) = \sin A \cos B + \cos A \sin B $$
   • For cosine: $$ \cos(A + B) = \cos A \cos B - \sin A \sin B $$

3. Examine General Solutions

   The general solution for trigonometric equations is expressed as:

   • For sine: $$ \sin x = 0 \Rightarrow x = n\pi, \ n \in \mathbb{Z} $$
   • For cosine: $$ \cos x = 0 \Rightarrow x = \frac{\pi}{2} + n\pi, \ n \in \mathbb{Z} $$
   • For tangent: $$ \tan x = 0 \Rightarrow x = n\pi, \ n \in \mathbb{Z} $$

4. Utilize Identities for Simplification

   Use identities such as:

   • Reciprocal identities, e.g.: $$ \csc x = \frac{1}{\sin x}, \ \sec x = \frac{1}{\cos x}, \ \cot x = \frac{1}{\tan x} $$
   • Pythagorean identities: $$ \sin^2 x + \cos^2 x = 1 $$

5. Apply Maximum and Minimum Value Formulas

   The maximum and minimum values of sine and cosine functions are discussed. For instance:

   • Maximum value: $$ \text{Max Value} = \frac{a}{\sqrt{a^2 + b^2}} $$
   • Minimum value: $$ \text{Min Value} = -\frac{a}{\sqrt{a^2 + b^2}} $$