Trigonometry Proving the statement is innocent

  • Thread starter maxtheminawes
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So (1+sinx)(1-sinx) = 1^2 - (sinx)^2 = cos2x. In summary, we can prove that (1+sinx)(1-sinx) = cos^2 by using the identity (a+b)(a-b) = a^2 - b^2 and the equation sin^2x+cos^2x=1.
  • #1
maxtheminawes
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Homework Statement


Prove this statement. (1+sinx)(1-sinx)=cos^2

Homework Equations


sin^2x+cos^2x=1


The Attempt at a Solution


statement Reason
(1+sinx)(1-sinx) Given
1^2-sinx+sinx+sinx^2 GCF
1+sinx^2 Cancel
1+ (1/cscx) I'm stuck after that
 
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  • #2
Hi,
Look at your negatives again, you're missing one, which is practically the final step towards finding the solution.
 
  • #3
maxtheminawes said:

Homework Statement


Prove this statement. (1+sinx)(1-sinx)=cos^2

Homework Equations


sin^2x+cos^2x=1

The Attempt at a Solution


statement Reason
(1+sinx)(1-sinx) Given
1^2-sinx+sinx+sinx^2 GCF
1+sinx^2 Cancel
1+ (1/cscx) I'm stuck after that

You can simply use (a+b)(a-b) = a2 - b2, as it's considered a "commonly understood" identity.
 

1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles.

2. What does it mean to prove a statement in trigonometry?

To prove a statement in trigonometry means to use logical reasoning and mathematical principles to show that a given statement or equation is true for all possible cases.

3. How do you prove the statement is innocent in trigonometry?

To prove a statement is innocent in trigonometry, you would need to show that the statement is true for all possible values of the variables involved, using established trigonometric identities, properties, and theorems.

4. What are some common methods of proving statements in trigonometry?

Some common methods of proving statements in trigonometry include using algebraic manipulation, the Pythagorean theorem, trigonometric identities, and the laws of sine and cosine.

5. Why is it important to prove statements in trigonometry?

Proving statements in trigonometry is important because it allows us to establish the validity of equations and solve complex problems accurately. It also helps to build a deeper understanding of the concepts and principles of trigonometry.

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