How do you express sin4θ+cot2θ−cos4θ in terms of non-exponential trigonometric functions?
1 Answer
Feb 1, 2016
Explanation:
Rewrite to group the sine and cosine terms.
=sin4θ−cos4θ+cot2θ
Simplify the first two terms as a difference of squares.
=(sin2θ+cos2θ)(sin2θ−cos2θ)+cot2θ
Note that
=sin2θ−cos2θ+cot2θ
The first two terms can again be factored as a difference of squares.
=(sinθ+cosθ)(sinθ−cosθ)+cot2θ
Use the identity:
=(sinθ+cosθ)(sinθ−cosθ)+csc2θ−1
Again, the last two terms can be factored as a difference of squares.
=(sinθ+cosθ)(sinθ−cosθ)+(cscθ+1)(cscθ−1)