Proving the Identity: sinA/(1+cosA)=tan(A/2)

Thread starter brandon26
Start date Oct 12, 2005
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Identity

In summary, to prove the identity sinA/(1+cosA)=tan(A/2), we can use the half-angle identity for tangent and substitute tan(A/2) for sinA/(1+cosA). Proving identities in mathematics is important for manipulating and simplifying complex expressions and making connections between concepts. To check if a proof is correct, you can substitute values for A and ask for a review from a teacher or mathematician. Common mistakes to avoid when proving identities include not considering restrictions on variables and using incorrect algebraic principles. This identity can also be used to solve trigonometric equations and simplify expressions.

Oct 12, 2005

brandon26

Prove the identity:

sinA / (1+cosA) = tan (A/2).

Im going no where with this, please help?

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Oct 12, 2005

Fermat

Homework Helper

use the double angle formula for cos2ø.

Oct 12, 2005

brandon26

Sorry I don't understand. And I am trying to apply the double angle formulae but I am just getting confused.

Oct 12, 2005

brandon26

Problem solved...No need to reply

Related to Proving the Identity: sinA/(1+cosA)=tan(A/2)

1. Can you explain the steps to prove the identity sinA/(1+cosA)=tan(A/2)?

To prove this identity, we can use the half-angle identity for tangent, which states that tan(A/2) = sinA/(1+cosA). Therefore, we can substitute tan(A/2) for sinA/(1+cosA) and the identity is proven.

2. What is the importance of proving identities in mathematics?

Proving identities in mathematics is important because it allows us to manipulate and simplify complex expressions, which can help us to solve equations and make connections between different concepts in mathematics.

3. How can I check if my proof of this identity is correct?

One way to check if your proof is correct is by substituting different values for A and seeing if the original expression and the simplified expression are equal. You can also ask a teacher or fellow mathematician to review your proof.

4. Are there any common mistakes to avoid when proving identities?

One common mistake is to manipulate both sides of the equation without considering the restrictions on the variable. Another mistake is to use incorrect algebraic principles, such as dividing by zero or canceling out terms that are not identical.

5. Can this identity be used to solve trigonometric equations?

Yes, this identity can be used to solve trigonometric equations by simplifying the expression and then using other trigonometric identities to solve for the unknown variable. It can also be used to prove other identities and to simplify complex trigonometric expressions.