tan^2x-sec^2x=?
Can you show me how to answer this?
change tan and sec to sin/cos, and 1/cos
combine the terms: the numerator should be something like sin^2 -1 which is equal to cos squared. Reduce.
To find the value of tan^2x - sec^2x, we can start by using the trigonometric identity for secant-squared:
sec^2x = 1 + tan^2x
Substituting this identity into the original equation, we have:
tan^2x - sec^2x = tan^2x - (1 + tan^2x)
Distributing the negative sign, we get:
tan^2x - sec^2x = tan^2x - 1 - tan^2x
Simplifying further, we can cancel out the tan^2x terms:
tan^2x - sec^2x = -1
Therefore, tan^2x - sec^2x equals -1.
To solve the expression tan^2x - sec^2x, we can use the trigonometric identities.
1. Start with the Pythagorean identity: sec^2x = 1 + tan^2x.
- This identity relates the square of the secant function to the square of the tangent function.
2. Substitute the Pythagorean identity into the original expression: tan^2x - (1 + tan^2x).
- This step simplifies the expression by replacing sec^2x with its equivalent expression.
3. Simplify the expression using algebra: tan^2x - 1 - tan^2x.
- Distribute the negative sign to both terms inside the parentheses.
4. Combine like terms: (tan^2x - tan^2x) - 1.
- Subtract tan^2x from itself, which results in zero.
5. Further simplify: - 1.
- Subtract 1 from 0.
Therefore, the expression tan^2x - sec^2x simplifies to -1.