**Trigonometric Ratios of Compound Angles**

The sum or difference of two or more
angles is said to be a **compound angle**.
If **A** and **B** are two angles then **A + B**
or **A - B **are known as the **compound angles**.

We express the **trigonometrical ratios of compound angle** A + B and A - B in terms
of trigonometrical ratios of the angles A and B.

The trigonometrical ratios of the angles
A + B and A - B are known as the **addition**
and **subtraction formula**
respectively.

**Trigonometric Ratios of Compound Angle A + B (Addition Formula)**

Let a revolving line start from OX and
trace out an angle XOY = A and revolve further through an angle YOZ = B.
Therefore, ∠XOZ = A + B.

Let, P be any point on OZ. Draw PM
perpendicular to OX and PN perpendicular to OY. From N draw NQ perpendicular to
OX and NR perpendicular to PM.

Here,
∠RPN = 90° - ∠PNR [∵ NR⊥MP]

= ∠RNO [∵ PN⊥OY]

= ∠NOQ [∵ RN ∥ OX]

= A

Again,
RMQN is a rectangle. So, MR = QN and RN = MQ.

Now
from right angle ΔOMP,

**Tangent Formula of Compound Angle (A + B)**

**Cotangent Formula of Compound Angle (A + B)**

**Trigonometric Ratios of Compound Angle A – B (Subtraction
Formula)**

Let a revolving line start from OX and
trace out an angle XOY = A and then revolve back through an angle YOZ = B.
Therefore, ∠XOZ = A - B.

Let, P be any point on the line OZ. Draw
PM perpendicular to OX and PN perpendicular to OY. From N draw NQ perpendicular
to OX and NR perpendicular to MP produced.

Here,
∠RPN = 90° - ∠PNR [∵ PR⊥NR]

= ∠RNY [∵ PN⊥OY]

= ∠XOY [∵ OX ∥ NR]

= A

Again,
QMRN is a rectangle. So, QN = MR and QM = NR.

Now
from right angle ΔOMP,

**Tangent Formula of Compound Angle (A ****–**** B)**

**Cotangent Formula of Compound Angle (A - B)**

**List of Trigonometric Formula for Compound Angles A + B and A –
B**

*Worked
Out Examples*

*Worked Out Examples*

*You can comment your
questions or problems regarding the trigonometric ratios of compound angles
here.*

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