# Factoring trigonometric equation

• sapiental
In summary, the conversation discusses the confusion over factoring an equation in a math book, specifically the transformation of (cos(t)sin(t) - (1 + sin(t))cos(t)) / (cos(t)cos(t) - (1 + sin(t))sin(t)) to (cos(t)(1+2sin(t))) / ((1 + sin(t)) (1 - 2sin(t))). The conversation also mentions the use of trig identities to prove the identity (cos t)(cos t) - (1 + sin t)(sin t) = (1 + sin t)(1 - 2 sin t).
sapiental
Hi,

I'm having trouble understanding how my math book factored the following equation.

[(cos(t)sin(t) - (1 + sin(t))cos(t)) / (cos(t)cos(t) - (1 + sin(t))sin(t))]

to get

[(cos(t)(1+2sin(t))) / ((1 + sin(t)) (1 - 2sin(t)))]

I get the numerator but I don't understand what happened to the cosine in the denominator..

Any suggestions?

Thanks

I don't believe those are equal. For example, if you plug in t=0, the first expression is equal to -1, and the second is +1. Presumably it's just a typo.

Anyways, this is why you studied trig identities in precalc. Pretend you were given the following problem.

Prove the identity:
(cos t)(cos t) - (1 + sin t)(sin t) = (1 + sin t)(1 - 2 sin t)​

Last edited:
oh right

cos^2(x) + sin^2(x) = 1

thanks!

## 1. What is factoring in trigonometric equations?

Factoring in trigonometric equations is the process of rewriting a trigonometric equation in a simpler form by finding common factors and factoring them out. This is a useful technique for solving equations and simplifying expressions in trigonometry.

## 2. Why is factoring important in trigonometric equations?

Factoring is important in trigonometric equations because it allows us to solve equations and simplify expressions that would otherwise be difficult to solve. It also helps us to recognize patterns and relationships between different trigonometric functions.

## 3. How do you factor a trigonometric equation?

To factor a trigonometric equation, you need to first identify any common factors among the terms. Then, you can use algebraic techniques such as the distributive property or the difference of squares to factor out these common factors. It is also helpful to use trigonometric identities to simplify expressions and make factoring easier.

## 4. Can all trigonometric equations be factored?

No, not all trigonometric equations can be factored. Some equations may not have any common factors, or they may require more advanced techniques to factor. In some cases, factoring may not be necessary to solve the equation.

## 5. How does factoring help us solve trigonometric equations?

Factoring helps us solve trigonometric equations by simplifying them into a form that is easier to work with. It also allows us to use algebraic techniques to isolate the variable and solve for its value. In some cases, factoring can also help us to identify solutions that may not be apparent without factoring.

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