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"
sin^{2} x means "obtain the sine of x then square the result"
whereas
sin x^{2} means "square x then obtain the sine of x
squared".
Generally these four expressions
are not equivalent!
Example
4 

xcos^{2} x
+ 4x^{2} cos x sin x 
Strategy 
xcos^{2}
x and 4x^{2} 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 x^{2}
have x in common 
Find the common factor for
factors involving a variable. 
cos^{2} 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. 

xcos^{2} x
+ 4x^{2} 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.
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