To prove the identity cot(a) – cot(b) = (1 – cota * cotb) / (cota * cotb), we can start by manipulating the left side of the equation. Recall that the cotangent function is defined as: cot(x) = cos(x) / sin(x) Thus, we can express cot(a) and cot(b) as: cot(a) = cos(a) / sin(a) cot(b) … Read more
To find the slope of a line that passes through two points, you can use the slope formula, which is: Slope (m) = (y2 – y1) / (x2 – x1) In this case, you have the points (1, 4) and (0, 1). We can label these points as follows: (x1, y1) = (1, 4) (x2, … Read more
To compute the least common multiple (LCM) of √2 and √3, we need to understand how the LCM works with irrational numbers. The LCM of two numbers is the smallest number that is a multiple of both. For our irrational numbers, we can express them in terms of their square roots: √2 = 21/2 √3 … Read more
The slope-intercept form of a line is expressed with the equation: y = mx + b Where: y is the dependent variable (the value of y for given x) m represents the slope of the line x is the independent variable b is the y-intercept (the value of y when x is 0) In this … Read more
To solve the equation x² + 8x + 3 = 0 by completing the square, we first need to rewrite the equation in a more manageable form. 1. Start with the original equation: x² + 8x + 3 = 0 2. To complete the square, we want to focus on the quadratic and linear terms, … Read more
To determine the measure of angle ABD in trapezoid ABCD, we need to understand the properties of trapezoids and the relationships between their angles. A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. In our case, let’s assume that sides AB and CD are the parallel sides. 1. **Identify … Read more
Understanding the Probability of Rolling Three Different Numbers on Dice When you toss three dice, there are a total of 6 faces on each die, resulting in 6 imes 6 imes 6 = 216 possible outcomes. Calculating Favorable Outcomes To find the probability that all three numbers show different faces, we first calculate the number … Read more
A rational number is a type of number that can be expressed as a fraction or ratio of two integers, where the numerator is any integer and the denominator is a non-zero integer. In simpler terms, if you can write a number in the form of a/b, where a is an integer (which can be … Read more
To prove that: tan(45) × tan(45) × tan(45) × tan(45) = 1 × sin(2a) First, let’s simplify the left-hand side: We know that: tan(45) = 1 So, if we multiply tan(45) four times: tan(45) × tan(45) × tan(45) × tan(45) = 1 × 1 × 1 × 1 = 1 Now, we have: 1 = … Read more
To simplify the polynomial 8x² + 8x + 2 – 5x, we first need to combine like terms. Let’s break it down step by step: 1. Start with the original polynomial: 8x² + 8x + 2 – 5x 2. Combine the linear terms (the terms containing x): 8x + 2 – 5x = (8 – … Read more