# Trignometric identiy (LOADS o HELP ;D )

• clearlyjunk
In summary, using trigonometric identities and the periodicity of trigonometric functions, the given equation can be simplified to 0 = 0, showing that the equation is always true.
clearlyjunk

## Homework Statement

sin(pi +A) sec(pi-A)
--------- + ---------- = 0
cos (2pi + A) csc(2pi-A)

## Homework Equations

cscx=1/sinx
secx=1/cosx
sin(x+y)=sinxcosy+cosxsiny
sin(x-y)=sinxcosy-cosxsiny
cos(x+y)= cosxcosy-sinxsiny
cos(x-y)= cosxcosy+sinxsiny

## The Attempt at a Solution

LS
sin pi cosA + cosA sin pi || 1/cos pi cos A + sin pi sin A
------------------------ + --------------------------
cos 2pi cosA + sin 2pi sinA || 1/sin pi cos A - cos pi sin A

the || is a seperator of the fractions

^
if it helps, i got this one to equal zero :)

First off, use the identities that involve the sum of pi and an angle. E.g., sin(pi + A) = -sin(A) and cos(pi + A) = -cos(A). Also, cos(2pi + A) = cos(A) and so on.

Since all of the trig functions are periodic with period 2pi, f(2pi + A) = f(A), where f represents sine, cosine, tangent (yes I know that tangent's period is pi), and all the rest.

In the work you did, you have sin(pi) and cos(2pi) and all. Simplify those to 0 and 1, respectively.

$\frac {\sin (\pi+A)}{\cos(2\pi+A} \ + \ \frac{\sec(\pi-A)}{\csc(2\pi+A)} \ = \ 0$

## What is a trigonometric identity?

A trigonometric identity is an equation that is true for all values of a variable in a given domain. In other words, it is a statement that shows the relationship between different trigonometric functions.

## Why are trigonometric identities important?

Trigonometric identities are important because they help us simplify complex trigonometric expressions, solve equations, and prove other mathematical theorems. They also have practical applications in fields such as physics, engineering, and astronomy.

## How do you prove a trigonometric identity?

To prove a trigonometric identity, you need to use algebraic manipulations and properties of trigonometric functions to transform one side of the equation into the other. This can involve using double angle, half angle, or sum and difference identities, as well as simplifying using basic trigonometric rules.

## What are some common trigonometric identities?

Some common trigonometric identities include the Pythagorean identities, the sum and difference identities, the double angle identities, the half angle identities, and the product-to-sum identities. These can be used to simplify expressions, solve equations, and prove other identities.

## How can I improve my understanding of trigonometric identities?

To improve your understanding of trigonometric identities, it is important to practice solving problems and identifying which identities to use. You can also read textbooks or watch online tutorials to learn more about the properties and applications of trigonometric identities.

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