- #1
pbonnie said:Homework Statement
(question attached)Homework Equations
The Attempt at a Solution
Checking solution.. pretty sure I did this wrong.
(solution attached)
No, you're not getting it at all. On the right side, you have this:pbonnie said:Oh wow okay, I think I got it. Thank you very much
It's because you do not understand how to simplify fractions and rational expressions.pbonnie said:No matter what I do I can't get the answer.
If you multiply this back out do you get sin2(θ) - cos2(θ)?pbonnie said:So the numerator would be (sinƟ+cosƟ)(sinƟ+cosƟ)
Yes!pbonnie said:Oh! ab + b^2 would equal b(a+b)?
So the denominator would be cosƟ(sinƟ + cosƟ)?
Does (sinƟ+cosƟ)(sinƟ+cosƟ) multiply out to sin2Ɵ - cos2Ɵ?pbonnie said:Okay so now I have (sinƟ+cosƟ)(sinƟ+cosƟ)/cosƟ(sinƟ + cosƟ)
pbonnie said:So now I can actually cancel out (sinƟ + cosƟ) once on the top and once on the bottom, to get
sinƟ + cosƟ/cosƟ
From here I'm stuck again. I know the sinƟ/cosƟ would equal tan, but I'm not sure where the -1 comes from
So far, so good, but you need some more parentheses around the entire denominator, like so:pbonnie said:Ah sorry I had the right answer in my head but I wrote it out wrong. Didn't even notice.
(sinƟ+cosƟ)(sinƟ-cosƟ)/cosƟ(sinƟ + cosƟ)
Here you need some parentheses around the entire numerator, like so:pbonnie said:Then sinƟ-cosƟ/cosƟ
(A + B)/C is the same as A/C + B/C, and (A - B)/C is the same as A/C - B/C.pbonnie said:Now I'm stuck again.
pbonnie said:I'm doing different variations of substituting the quotient identity into the equation but I can't get the right order
A trigonometric identity is an equation that is true for all values of the variables involved. In other words, it is an equation that is always true, regardless of the specific values of the angles involved.
Proving a trigonometric identity is important because it helps to strengthen our understanding of the relationships between different trigonometric functions. It also allows us to simplify complex trigonometric expressions and solve more complicated problems.
The basic trigonometric identities are sine squared plus cosine squared equals one, tangent equals sine over cosine, and cotangent equals cosine over sine. These are often referred to as the Pythagorean identities.
To prove a trigonometric identity, you must manipulate the expression on one side of the equation using algebraic and trigonometric identities until it is equivalent to the expression on the other side of the equation. This process may involve using properties of trigonometric functions, such as the reciprocal, quotient, and Pythagorean identities.
The best approach for proving a trigonometric identity is to start by simplifying one side of the equation using known identities and properties. Then, work on the other side of the equation to make it look more like the simplified side. Continue this process until both sides of the equation are equivalent. It may also be helpful to use a step-by-step approach and keep track of each step taken.