# Trigonometry Help: Proving 1-cos@ / sin@ = tan(@/2)

• draotic
In summary, the purpose of proving 1-cos@ / sin@ = tan(@/2) is to demonstrate the relationship between the three basic trigonometric functions and aid in solving problems involving triangles and angles. This identity is derived using the fundamental and double angle identities, and can be used to solve trigonometric equations. There are various methods for proving this identity, and it can be applied in real-life situations such as navigation, engineering, and physics.
draotic

## Homework Statement

will sum1 prove this ...@=theta
1-cos@ / sin@ = tan(@/2)

## The Attempt at a Solution

i tried to do this
cos@ = cos^2(@/2) - sin^2 (@/2)
wat now?
...
thats doesn't get me anywhere

Last edited:
Since you have a half angle on the right side, you'll want to convert all angles into their half angle equivalents. For example, $$\sin(2x)=2\sin(x)\cos(x)$$ therefore $$\sin(\theta)=2\sin\left(\frac{\theta}{2}\right) \cos \left(\frac{\theta}{2}\right)$$

## 1. What is the purpose of proving 1-cos@ / sin@ = tan(@/2)?

The purpose of proving this trigonometric identity is to show the relationship between the three basic trigonometric functions: sine, cosine, and tangent. It also helps in solving various mathematical problems involving triangles and angles.

## 2. How is the identity 1-cos@ / sin@ = tan(@/2) derived?

This identity can be derived using the fundamental trigonometric identity, sin²@ + cos²@ = 1, and the double angle identity, sin2@ = 2sin@cos@. By substituting sin²@ = 1-cos²@ and sin2@ = 2sin@cos@, we get 1-cos@ / sin@ = (1-cos²@) / 2sin@cos@ = tan@/2.

## 3. Can this identity be used to solve trigonometric equations?

Yes, this identity can be used to solve trigonometric equations involving 1-cos@ / sin@, such as in proving other trigonometric identities or finding the values of unknown angles in a triangle.

## 4. Is there a specific method for proving this identity?

There are various methods for proving this identity, such as using the Pythagorean identities, double angle identities, or manipulating the given expression using algebraic techniques. The method used may vary depending on the complexity of the problem and personal preference.

## 5. How can I use this identity in real-life situations?

This identity can be useful in solving real-life problems involving angles and triangles, such as in navigation, engineering, and physics. It can also be used to simplify complex trigonometric expressions and equations, making them easier to solve.

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