Trigonometry Proving the statement is innocent

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The discussion revolves around proving the identity (1+sinx)(1-sinx)=cos^2 using trigonometric identities. Participants suggest applying the difference of squares formula, a^2 - b^2, to simplify the expression. The initial steps involve expanding the left side and recognizing the relationship between sine and cosine through the fundamental identity sin^2x + cos^2x = 1. A participant notes a mistake in the negative signs during the simplification process, which is crucial for arriving at the correct conclusion. The conversation emphasizes the importance of careful algebraic manipulation in trigonometric proofs.
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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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Hi,
Look at your negatives again, you're missing one, which is practically the final step towards finding the solution.
 
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.
 

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