Use euler's formula to derive the identity. (note that if a, b, c, d are real numbers, a + bi = c + di means that a = c and b = d. simplify your answer completely.) sin(2θ) = 2 sin(θ) cos(θ) using euler's formula, we have ei(2θ) = + i sin(2θ). on the other hand, ei(2θ) = (eiθ)2 = + i sin(θ) 2 = (cos2(θ) − sin2(θ)) + i sin(θ) . equating correct: your answer is correct. parts, we find sin(2θ) = 2 sin(θ) cos(θ).

Answer with Step-by-step explanation:

We have to prove that

by using Euler's formula

Euler's formula :

By using Euler's identity, we get

Comparing imaginary part on both sides

Then, we get

Hence, proved.

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

step-by-step explanation:

gym b charges $1.05 less per hour than gym a.