Question

prove the identity.

\\(\tan (\pi - x) = -\tan x\\)

click here to learn more about writing a trigonometric proof.

statement | reason
\\(\tan (\pi - x)\\) |
= | select

select options:
algebraic transformation
reciprocal identities
quotient identities
pythagorean identities
odd and even identities
evaluation of an expression
sum and difference identities

Explanation:

Express tangent using quotient identities

Using the Quotient Identities knowledge point

$$ \tan(\pi - x) = \frac{\sin(\pi - x)}{\cos(\pi - x)} $$

Apply sum and difference identities

Using the Sum and Difference Identities knowledge point

$$
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$$

Simplify the quotient expression

Using the Trigonometric Proofs knowledge point

$$ \frac{\sin(\pi - x)}{\cos(\pi - x)} = \frac{\sin x}{-\cos x} = -\frac{\sin x}{\cos x} = -\tan x $$

Answer:

To prove the identity \(\tan(\pi - x) = -\tan x\), the first step in the proof is:

• Statement: \(\frac{\sin(\pi - x)}{\cos(\pi - x)}\)
• Reason: Quotient identities