Is 1-(sin^6x+cos^6x)=(3sin^2x)(cos^2x) a Valid Trigonometric Identity?

In summary, verifying a trigonometric identity means proving its truth for all values of the variables involved. This is important for ensuring the accuracy of mathematical equations. The process involves using algebraic and trigonometric identities to manipulate the given equation until it is transformed into a known identity or is proven to be true. Some common identities that can be used include the Pythagorean, reciprocal, quotient, and double angle identities. If you are struggling, you can try different approaches or seek help from a teacher or tutor.
  • #1
larymac47
1
0
1-(sin^6x+cos^6x)=(3sin^2x)(cos^2x)

I got this far:

1-(sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x)=(3sin^2x)(cos^2x)
1-(sin^4x-sin^2xcos^2x+cos^4x)=(3sin^2x)(cos^2x)
 
Last edited:
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  • #2
I'd start by manipulating one of the sides.
 

FAQ: Is 1-(sin^6x+cos^6x)=(3sin^2x)(cos^2x) a Valid Trigonometric Identity?

What does it mean to verify a trigonometric identity?

Verifying a trigonometric identity means to prove that the equation is true for all values of the variables involved.

Why is it important to verify trigonometric identities?

Verifying trigonometric identities is important because it helps to ensure the accuracy and validity of mathematical equations and calculations.

What is the process for verifying a trigonometric identity?

The process for verifying a trigonometric identity involves manipulating the given equation using algebraic and trigonometric identities, until it is transformed into a known identity or is proven to be true.

What are some common trigonometric identities that can be used to verify equations?

Some common trigonometric identities that can be used to verify equations include the Pythagorean identities, the reciprocal identities, the quotient identities, and the double angle identities.

What should I do if I am having trouble verifying a trigonometric identity?

If you are having trouble verifying a trigonometric identity, you can try using different identities or approaches, breaking the equation into smaller parts, or seeking help from a teacher or tutor.

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