Use compound angle formulae to find sin 15 and cos 15 in form of [ surd a (surd b + c) ] . hence, find tan 15 in the simplest surd form

see explanation

Step-by-step explanation:

Using the difference formulae for sine and cosine

sin(x - y) = sinxcosy - cosxsiny

cos(x - y) = cosxcosy + sinxsiny

sin15° = sin(45 - 30)°

sin(45 - 30)°

= sin45°cos30° - cos45°sin30°

= × - ×

= -

=

----------------------------------------------------------------------------------

cos15° = cos(45 - 30)°

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= × + ×

= +

=

-------------------------------------------------------------------------------------

tan15° =

= ×

=

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator, that is ( - )

=

=

=

= 2 -

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.