Sum and Difference Identities Calculator
'Sum and Difference Identities Calculator' is an online tool that helps to calculate trigonometric identities. We have six main sum and difference formulas for the trigonometric functions including the sine function, cosine function, and tangent function.
What is Sum and Difference Identities Calculator?
Online calculator helps you to calculate the Sum and Difference Identities in a few seconds. The sum and difference formulas in trigonometry are used to find the value of the trigonometric functions at specific angles where it is easier to express the angle as the sum or difference of unique angles (0°, 30°, 45°, 60°, 90°, and 180°).
Sum and Difference Identities Calculator
NOTE: Enter the values upto three digits only.
How to Use Sum and Difference Identities Calculator?
Please follow the below steps to find the trigonometric identities:
- Step 1: Enter the angles in the given input box.
- Step 2: Click on the "Calculate" button to find the trigonometric identities
- Step 3: Click on the "Reset" button to find the trigonometric identities for different angles.
How to Find Sum and Difference Identities?
Identities involving the sum and difference of two angles and apply to the fundamental trigonometric functions, i.e., sin(A ± B), cos(A±B), tan(A±B).
For example, sin(A ± B) = sinA cosB ± cosA sinB. Similarly for cosine, tangent trignomteric functions also.
Solved Examples on Sum and Difference Identities Calculator
Example 1:
Find the sum and difference for cos(A ± B), if the angles A = 0°, B = 90° ?
Solution:
cos(A + B) = cosA cosB - sinA sinB
cos(0 + 90) = cos0° cos90° - sin0° sin90°
cos90° = 0 - 0
cos90° = 0
cos(A - B) = cosA cosB + sinA sinB
cos(0 - 90) = cos0° cos90° + sin0° sin90°
cos(-90°) = 0 + 0
cos(-90°) = 0
Example 2:
Find the sum and difference for cos(A ± B), if the angles A = 45°, B = 45° ?
Solution:
cos(A + B) = cosA cosB - sinA sinB
cos(45 + 45) = cos45° cos45° - sin45° sin45°
cos90° = 1/2 - 1/2
cos90° = 0
cos(A - B) = cosA cosB + sinA sinB
cos(45 - 45) = cos45° cos45° + sin45° sin45°
cos(0) = 1/2 + 1/2
cos0° = 1
Example 3:
Find the sum and difference for cos(A ± B), if the angles A = 45°, B = 0° ?
Solution:
cos(A + B) = cosA cosB - sinA sinB
cos(45 + 0) = cos45° cos0° - sin45° sin0°
cos45° = 1/√2(1) - 1/√2(0)
cos45° = 1/√2
cos(A - B) = cosA cosB + sinA sinB
cos(45 - 0) = cos45° cos0° + sin45° sin0°
cos(45) = 1/√2(1) + 1/√2(0)
cos45° = 1/√2
Similarly, you can try the Sum and Difference Identities Calculator to determine the sum and difference for:
1) cos(A ± B) if A = 60° and B = 90°
2) sin(A ± B) if A = 180° and B = 30°