Expanding Using Sum/Difference Formulas Calculator

Created By : Vipul Patel

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 01, 2025

Utilize expanding using a sum/differences formulas calculator tool is the best and most convenient tool and gives the answer in a fraction of seconds. You must provide the input in the input field and click on the calculate button for the instant results.

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Simplify the Trig Equation using Sum/Differences Formulas Calculator: Need to simplify the trig equation using sum/differences in a blink of an eye. Then use our expanding using sum/differences calculator tool for that. And also learn the process of how to simplify the trig equations using the sum/differences formulas manually and in an easy way along with some solved examples.

How to Expand Trig Equations using Sum/Difference Formulas?

To help you in solving the trig equations using sum/difference formulas, we are providing you step-by-step process below.

  • First, write down the equation that was given in the problem.
  • Then, apply the formula of sum/differences in the given equation.
  • After simplifying it we get the answer.

Examples:

Question 1: Simplify the equation, sin 20°cos 40° + cos 20°sin 40°

Solution:

Given the trig equation,

sin 20°cos 40° + cos 20°sin 40°

Now, apply the sum formula,

sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

As per the formula, 

sin 20°cos 40° + cos 20°sin 40° 

= sin(20°+ 40°)

= sin(60°)

= √3 /2 

Therefore, sin 20°cos 40° + cos 20°sin 40° = √3 /2 .

Question 2: Simplify the equation, sin 30°cos 50° - cos 30°sin 50°

Solution:

Given the trig equation,

sin 30°cos 50° - cos 30°sin 50°

Now, apply the difference formula,

sin(x - y) = sin(x)cos(y) - cos(x)sin(y)

As per the formula, 

sin 30°cos 50° - cos 30°sin 50°

= sin(30°- 50°)

= sin(-20°)

= -0.015

Therefore, sin 30°cos 50° - cos 30°sin 50° = -0.015.

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FAQs on Expanding Using Sum/Difference Formulas Calculator

1. What are sum/difference formulas of sine?

sin(x + y) = sin(x)cos(y) + cos(x)sin(y).

sin(x - y) = sin(x)cos(y) - cos(x)sin(y).

2. How do you simplify an equation?

We simplify an equation by expanding the brackets and simplifying the resulting expression by collecting the likely terms.

3. How to use simplify using a sum/difference calculator?

For that, you need to give the inputs in the input fields and click on the calculate button so that get the answer instantaneously.

4. What are the steps used to simplify the trig equation using sum/difference formulas?

  • First, write down the equation that was given in the problem.
  • Then, apply the formula of sum/differences in the given equation.
  • After simplifying it we get the answer.