options: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
problem_activity: Problem 1
Find
$${\mathrm{sin}(u-v)}$$
given
$${\mathrm{sin}(u)={8\over17}}$$
with
$${0\leq u \leq {\pi\over2}}$$
and
$${\mathrm{cos}(v)=-{24\over25}}$$
with
$${\pi \leq v \leq {3\pi\over2}}$$
.
Problem 2
Evaluate:
$${\mathrm{sin}(-15^{\circ})}$$
$${\mathrm{cos}(15^{\circ})}$$


correct_option_index: 0