Question

\[\cot \dfrac{{A + B}}{2} \times \tan \dfrac{{A - B}}{2} = \]
A. \[\dfrac{{a + b}}{{a - b}}\]
B. \[\dfrac{{a - b}}{{a + b}}\]
C. \[\dfrac{a}{{a + b}}\]
D. None of these

Answer 1

Hint: Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Slope, usually referred to as rise over run, is the "steepness" of the line. A point on the y-axis known as an intercept is where the line's slope passes. It is a place on the y-axis where a straight line or a curve cross.
It is frequently useful to visualize the slope and intercept of the lines that intersect your equation while solving equations with variables. Plotting these two lines reveals that they cross at the coordinates \[\left( {0,0} \right)\] and\[\left( {1,1} \right)\], respectively. As a result, the problem can only have one solution, which is\[\left( {\dfrac{{a + b}}{{ab}}} \right)\].
A variable is a letter or symbol that stands in for any individual integer in a group of two or more. A constant is a letter or symbol that stands for a single particular number, whether it is known or unknown.

Complete step by step solution: The equation is \[\tan \dfrac{{A - B}}{2}\]
This can also be written as,
\[\dfrac{{a - b}}{{a + b}}\cot \dfrac{C}{2}\]
\[\dfrac{{a - b}}{{a + b}}\tan (\dfrac{{A + B}}{2})\]
Then, the equation becomes,
\[\tan \dfrac{{A - B}}{2}\cot \dfrac{{A + B}}{2} = \dfrac{{a - b}}{{a + b}}\]

So, Option ‘B’ is correct

Note: When solving inequalities, it is often helpful to put them into an expression in terms of pairs of coefficients.
Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Both mathematical phrases, equations and inequalities, are created by connecting two expressions.
Use inverse operations to first undo the addition or subtraction in a two-step inequality, and then undo the multiplication or division. Subtraction is the opposite operation to addition, and vice versa.