Tan (arcsec x + 3) - 3

📌 CONCEPT: Inverse trigonometric functions are used to find the angle whose trigonometric ratio is given. They are denoted by the prefix 'arc' in front of the trigonometric function. For example, arcsec x is the angle whose secant is x.

📐 RULE / FORMULA: The formula tan(∠A) = tan(∠B + ∠C) can be used here. Using the identity tan(A + B) = (tan A + tan B)/(1 - tan A tan B), we can write tan(∠A) = (tan ∠B + tan ∠C)/(1 - tan ∠B tan ∠C).

💡 WORKED EXAMPLE: Given tan(∠A) = 3 and ∠C = π/3, we know ∠B = arcsec(x + 3). Using the formula tan(∠A) = (tan ∠B + tan ∠C)/(1 - tan ∠B tan ∠C) and the given values, we can solve for tan(∠B).

⚠️ COMMON MISTAKE: Students often get confused between the trigonometric functions and their inverses, and may use the original function instead of its inverse. Also, they might forget to use the correct identity or formula in the given problem.