Use of Basic Addition Formulae of Trigonometry

Basic Addition Formulae of Trigonometry

Sine of Sum and Difference:

The sine of the sum of two angles can be expressed algebraically as: sin(A + B) = sinA.cosB + cosA.sinB
The sine of the difference of two angles is expressed as: sin(A - B) = sinA.cosB - cosA.sinB
Notice the patterns within these formulas, as understanding these will help you deduce them during calculations.

Cosine of Sum and Difference:

The formula for the cosine of the sum of two angles is: cos(A + B) = cosA.cosB - sinA.sinB
The cosine of the difference of two angles is given by: cos(A - B) = cosA.cosB + sinA.sinB
Observe the change in sign depending upon whether the angles are being added or subtracted.

Tangent of Sum and Difference:

The tangent of the sum of two angles is given by: tan(A + B) = (tanA + tanB) / (1 - tanA.tanB)
For the tangent of the difference of two angles, the formula is: tan(A - B) = (tanA - tanB) / (1 + tanA.tanB)
Remember that tan(x) is the ratio of sin(x) and cos(x).

Using the Basic Addition Formulas:

The addition formulas can be used to simplify trigonometric expressions or find the values for larger angles given some known smaller angles.
They are often helpful in solving trigonometric equations and verifying trigonometric identities.
Use the symmetry properties of the sine and cosine functions to derive the addition formulas for negative angles as well as for subtracting angles.
Always keep in mind that the trigonometric functions are cyclic, and watch out for angles that are over 90 degrees or less than 0 degrees. Consider using reference angles or the unit circle if you’re having trouble finding a trigonometric function’s value.