Question

Rewrite the following operations in their multiplication forms:
a. cos α + cos 2α + cos 3α
b. sin α + sin 2α + sin 3α + sin 4α

Answer 1

Step-by-step explanation:

a) cos @ + 2 cos @ + cos (2@+@)

=cos @ + 2cos @ + cos 2@ sin @ + sin 2@ cos @

=3cos @ + cos 2@ sin @ + sin @ cos 2@.

b) Similarly, it is

sin @ + 2sin@ cos @ + sin (2@+@) + sin (2@+2@)

=sin @ + 2sin @ + sin2@ cos @ + cos 2@ sin @ + sin 2@cos @ + cos 2@ sin @

=3 sin @ + 2sin 2@ cos @ +2cos 2@ sin @.

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