options: 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.

Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
problem_activity: Problem 1
Prove the cofunction identity of:
$${\mathrm{cos}\left({\pi\over2}-x\right)=\mathrm{sin}x}$$
Using the sum or difference formula.
Problem 2
Solve:
$${\mathrm{sin}\left(x+{\pi\over4}\right)+1=\mathrm{sin}\left({\pi\over4}-x\right)}$$
for
$${0 \leq x \leq 2\pi}$$
.


correct_option_index: 1