# Trig' Identities - Addition Formulae

• Maatttt0
In summary, the conversation discusses finding the exact value of cos(C + D) given that cos C = 12/13 and sin D = 3/5. The attempt at a solution involved using the Addition Formulae, but there was a mistake in the input. The error was corrected by using the identity sin^2x + cos^2x = 1 to find the exact values of sin(C) and sin(D).
Maatttt0
[STRIKE]

## Homework Statement

Given that cos C = 12/13 where C is a reflex and sin D = 3/5 where D is acute, find the exact value of cos ( C + D ).

## The Attempt at a Solution

I used the Addition Formulae: cos(A+B) = cosAcosB-sinAsinB

cos(12/13)cos(2/5) - sin(1/13)sin(3/5) = 0.999831...

As it says "exact value" I assume my long decimal answer is incorrect. I have inputed it all straight into my calculator. Help me please [/STRIKE]

Sorry - I've worked out my silly mistake. Thank you for looking

Last edited:
First off, you're not looking to find

cos(12/13)cos(2/5) - sin(1/13)sin(3/5)

you want to find

cos(C)cos(D) - sin(C)sin(D).

You are given the values of cos(C) and cos(D) in exact for. So your next step is to find the exact values of sin(C) and sin(D). There is one identity that is helpful here, can you think of which one?

Thank you for the help JeSuisConf but I've spotted the error.. Silly me, was making it far complicated than it actually is..

Thank you for looking though

## What are "Trig' Identities - Addition Formulae"?

"Trig' Identities - Addition Formulae" refers to a set of mathematical equations that involve trigonometric functions, such as sine, cosine, and tangent. These identities are used to simplify and solve trigonometric expressions and equations.

## What is the addition formula for sine?

The addition formula for sine states that sin(A + B) = sin(A)cos(B) + cos(A)sin(B). This formula is used to find the sine of the sum of two angles, A and B.

## How do I use the addition formula for cosine?

To use the addition formula for cosine, you can substitute the values of the two angles, A and B, into the formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B). This will give you the cosine of the sum of the two angles.

## What is the addition formula for tangent?

The addition formula for tangent is tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B)). This formula can be used to find the tangent of the sum of two angles, A and B.

## Can I use "Trig' Identities - Addition Formulae" to solve any trigonometric equation?

Yes, "Trig' Identities - Addition Formulae" can be used to solve a wide range of trigonometric equations. However, some equations may require additional identities or techniques to solve them completely.

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