Trigonometric Functions of Compound Angles. Compound Angle Formulae. Compound Angle Formulae. (A) Sum and Difference Formulae. If we replace B by (-B) in formula of sin(A – B), we have. If we replace A by ( /2 - A ) in the formula of sin(A - B), we have.

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If we replace B by (-B) in formula of sin(A – B), we have

If we replace A by (/2 - A) in the formula of sin(A - B), we have

By substituting (- B) in the formula of cos(A + B), we have

From the quotient relation and the above formulae,

By substituting (-B) for B in the formula tan(A + B)

Exercise 7.1

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Exercise 7.2

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The Subsidiary Angles

The Subsidiary Angles

The expression acos + bsin

may always be converted into the forms rsin( ±α) or rcos( ±β) where r is a positive constant.

α and β are called the subsidiary angles.

Exercise 7.3

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Sums and Products of Trigonometric Functions

+)

-)

+)

-)

If we put A + B = x and A – B = y, express in terms of x and y.

If we put A + B = x and A – B = y, express in terms of x and y.

Exercise 7.4

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Elimination of Angles

If we have two or more equations, each containing a certain variable, the process of finding an equation from which that variable isexcluded is called elimination.

Identities to be used in this section.

General Solutions of Trigonometric Equations

Inverse Trigonometric Functions

Inverse Trigonometric Functions

Inverse Trigonometric Functions

General Solutions

where n is any integer and is any root of cos = k.

where n is any integer and is any root of sin = k.

where n is any integer and is any root of tan = k.