What is tan formula identity?

The tangent (tan) formula identity states that the tangent of an angle (θ) is equal to the sine of that angle divided by the cosine of that angle. This is a fundamental trigonometric identity.

Here's a breakdown:

• The Formula:

  tan θ = sin θ / cos θ

• Explanation:

  • tan θ represents the tangent of the angle θ.
  • sin θ represents the sine of the angle θ.
  • cos θ represents the cosine of the angle θ.

• Importance: This identity allows you to calculate the tangent of an angle if you know its sine and cosine. It's also crucial for simplifying trigonometric expressions and solving trigonometric equations.

• Other Related Identities (For Context): While the core answer is above, here are other related trigonometric identities:

  • Reciprocal Identities:
    • cot θ = 1 / tan θ = cos θ / sin θ
  • Pythagorean Identities: These link sine, cosine, and tangent indirectly:
    • sin² θ + cos² θ = 1
    • 1 + tan² θ = sec² θ
    • 1 + cot² θ = csc² θ

The tan θ = sin θ / cos θ identity is essential for understanding and working with trigonometric functions.