What is cos4θ+sin3θ in terms of non-exponential trigonometric functions?

1 Answer
Jul 8, 2016

=18(3+4cos2θ+2cos4θ+6sinθ2sin3θ)

Explanation:

We will use the identities

>2cos2θ=(1+cos2θ)

>4sin3θ=3sinθsin3θ

The given expression

=cos4θ+sin3θ

=14(4cos4θ+4sin3θ)

=14((2cos2θ)2+3sinθsin3θ)

=14((1+cos2θ)2+3sinθsin3θ)

=14(1+2cos2θ+cos22θ+3sinθsin3θ)

=14(1+2cos2θ+12(1+cos4θ)+3sinθsin3θ)

=14(32+2cos2θ+cos4θ+3sinθsin3θ)

=18(3+4cos2θ+2cos4θ+6sinθ2sin3θ)