- #1
thorpelizts
- 6
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solve for
tan^4x + tan^2x = sec ^4x - sec^2x
i solved and ended up with RIHS= tan^4x?
tan^4x + tan^2x = sec ^4x - sec^2x
i solved and ended up with RIHS= tan^4x?
Last edited by a moderator:
thorpelizts said:solve for
tan^4x + tan^2x = sec ^4x - sec^2x
i solved and ended up with RIHS= tan^4x?
A trigonometric equation is an equation that involves trigonometric functions such as sine, cosine, and tangent. It typically involves finding the unknown angle or side length in a triangle.
The steps for solving a trigonometric equation are:
1. Rewrite the equation using trigonometric identities, if necessary.
2. Simplify the equation by combining like terms.
3. Isolate the trigonometric function by moving all other terms to the other side of the equation.
4. Solve for the unknown angle or side length using inverse trigonometric functions.
5. Check your answer by plugging it back into the original equation.
Some common trigonometric identities used in solving equations include:
- Pythagorean identities: sin²x + cos²x = 1 and tan²x + 1 = sec²x
- Double angle identities: sin2x = 2sinx*cosx and cos2x = cos²x - sin²x
- Half angle identities: sin²(x/2) = (1 - cosx)/2 and cos²(x/2) = (1 + cosx)/2
The possible solutions to a trigonometric equation depend on the domain and range of the trigonometric function. In general, there can be infinite solutions for trigonometric equations. However, if the domain is restricted, there may be a finite number of solutions.
Extraneous solutions occur when a value satisfies the equation but is not a valid solution. This can happen when taking the inverse of a trigonometric function, as it may introduce additional solutions that do not work in the original equation. It is important to always check for extraneous solutions when solving trigonometric equations.