Subtraction Formulas

Subtraction is a fundamental arithmetic operation. Subtraction is a mathematical operation that involves subtracting a part of one number from another. The process of subtracting one number from another is known as subtraction.

What is Subtraction?

Subtraction is the operation in which we reduce the value. It is the process of taking away in order to make the number smaller. It is denoted by the '-' operator.

For example, 

We have 3 apples and we eat 2 apples. So there is only 1 apple left. Subtraction makes the number smaller. For example, 10 - 2 is 8. This means that we take away 2 parts from the 10 parts.

Subtraction Formula

When we perform subtraction there are some terms associated with it:

• Minuend: It is the number from which another number is subtracted. It is that number which is reduced by the subtrahend In the above example 10 is the minuend.

• Subtrahend: The number which is to be subtracted. Here 2 is the minuend.

• Difference: It is the result after the subtraction of two numbers.

The required subtraction formula is:

Subtraction Formulas in Trigonometry

Various subtraction formulas in trigonometry are:

Sin Subtracting Formula:

Sin subtraction formula of trigonometry is given as:

• sin(A - B) = sin A cos B - cos A sin B

Cos Subtracting Formula:

Cos subtraction formula of trigonometry is given as:

• cos(A - B) = cos A cos B + sin A sin B

Tan Subtracting Formula:

Tan subtraction formula of trigonometry is given as:

• tan(A - B) = (tan A - tan B) / (1 + tan A tan B)

Solved Examples on Subtraction Formulas

Example 1: If Ram's mother gave him 99 rupees to buy stationary, out of which he used 60 rupees. Then calculate the amount he left with.

Solution:

Total amount of money he has 99 rupees,

He spends 60 rupees.

Now, he left with (99-60) rupees = 39 rupees.

Example 2: Find the difference between 454 and 666.

Solution:

The difference between 454 and 666 is given by,

454 - 666 

= - (666 - 454) 

= -212

Example 3: If there are 67 apples and a dozen of Apples are distributed among some children. How many apples are there? 

Solution:

As we know 1 dozen = 12 units

So 12 apples have been distributed

Therefore the number of apples is 67 - 12 

= 55

Example 4: How much we should subtract from 1000 to get 90? 

Solution:

Let x be the subtrahend, then

1000 - x = 90

Therefore x = 1000-90 

= 910

Example 5: Find the value of 4/2 - 3 -6.

Solution:

According to BODMAS rule, 4/2 = 2

Then 

4/2 - 3 -6 = 2 - 3 - 6 

= -7

Example 6: Find cos 15°.

Solution:

We known that,

cos(a-b) = cosa.cosb + sina.sinb...(i)

Choose a = 45° and b = 30°

cos⁡15° = cos ⁡(45° - 30°)

Using formula from eq(i)

cos⁡15° = cos⁡45°cos⁡30° + sin⁡45°sin⁡30°

Substituting,

• cos⁡45° = 1/√2, and cos⁡30° = √3/2
• sin45° = √2, and sin⁡30° = 1/2

Putting these into the formula:

cos⁡15° = (1/√2)(√3/2) + (1/√2)(1/2)

cos15° = (√6 + √4)/4

Example 7: Find sin 15°.

Solution:

We known that,

sin(a-b) = sina.cosb - cosa.sinb...(i)

Choose a = 45° and b = 30°

sin15° = sin ⁡(45° - 30°)

Using formula from eq(i)

sin15° = sin45°cos⁡30° - cos⁡45°sin⁡30°

Substituting,

• cos⁡45° = 1/√2, and cos⁡30° = √3/2
• sin45° = √2, and sin⁡30° = 1/2

Putting these into the formula:

sin ⁡15° = (1/√2)(√3/2) - (1/√2)(1/2)

sin 15° = (√6- √4)/4

Practice Problems on Subtraction

1. Subtract 25 from 100.

2. What is the difference between 345 and 123?

3. If you have 500 apples and give away 275, how many apples are left?

4. Subtract 19 from 87.

5. Find the difference between 789 and 456.

6. If a shopkeeper had 150 pens and sold 90, how many pens are left?

7. Subtract 92 from 160.

8. What is the difference between 1000 and 234?

9. If a student scored 78 marks out of 100 and lost 22 marks, what is his final score?

10. Subtract 1234 from 5678.