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Factorization

Trigonometric Functions

Before you begin factorising make sure you understand some differences in notation.

2sin x means "obtain the sine of x then double the result" whereas
sin 2x means "double x and then obtain the sine of twice x"
sin² x means "obtain the sine of x then square the result" whereas
sin x² means "square x then obtain the sine of x squared".

Generally these four expressions are not equivalent!

Example 4
xcos² x + 4x² cos x sin x	Strategy
xcos² x and 4x² cos x sin x	Consider each product separately, but watch out for sums which may be in common.
1 and 4 have a HCF of 1	Find the highest common factor of the numeric parts of the product expressions.
x and x² have x in common	Find the common factor for factors involving a variable.
cos² x and cos x sin x have cos x in common.	Find the common factor for factors which involve trigonometric factors.
Hence xcos x is the largest common factor.
xcos² x + 4x² cos x sin x =xcos x(cos x) + xcos x(4x sin x) = xcos x(cos x + 4x sin x)	Put the parts together.

Try these.

Exercise 4

Factorise these then check your answers.

sin 2x - cos 2x
cos² 3x + cos 3x sin 2x
(x - 1)²sin² 4y - sin 4y + xsin 4y
tan² z cos z - 3 sin z

<< Polynomials | Factorisation Index | Exponential Functions >>

Factorization

Trigonometric Functions

Example 4

Strategy

Exercise 4