Introduction To Trigonometry

To solve the problem, we are given:

1. Using Standard Trigonometric Values:
We know that:

This implies:

2. Solving the System of Equations:
Add the two equations:



Now substitute into :

Final Answer:

To solve the problem, we need to find the value of given that , and .

1. Using the Identity:
We are given .
Divide both sides of the equation by (which is not zero in the given range):

2. Verifying the Angle:
The equality occurs at , where indeed .

Final Answer:
The value of is 1.

To solve the problem, we are given:

We are to find .

1. Determine Angle A:
From , we know:

2. Use the Value of :
Given , we recognize that:

3. Solve for :

Final Answer:
The value of is .

To solve the problem, we need to evaluate the expression:

1. Use Trigonometric Identity:
We know that:

So the expression becomes:

2. Express in Terms of Sine and Cosine:


So,

Final Answer:
The value of the expression is

To solve the problem, we are given:

• Right triangle with
• Given:

1. Understanding :
In a right triangle,
So,

2. Using Pythagoras Theorem:
Let the sides be: - Opposite to (AB) = 5 units
- Adjacent to (BC) = 12 units
Then by Pythagoras theorem:

Final Answer:
The length of the hypotenuse is .

To solve the problem, we need to find the value of given that and .

1. Use Standard Trigonometric Values:
We know the standard values:

2. Substitute the Values:

3. Take LCM to Simplify:
To simplify the sum:

Final Answer:
The value of is .