It can be shown by induction that the nth derivative of the sine function is given by the formula d" (sin x) = (-1)"-1)/2 cos x, n odd (-1)"/2 sinx, n even. dx" Persuade yourself that this formula is correct and obtain a similar formula for the nth derivative of the cosine function.

Q: How is the addition formula used in deriving the formula (sin x) , = cos x?

A:

Q: sec(t) – cos(t) - Simplify to a single trig function. sin(t)

A: Using trigonometric formulas

Q: If sin-1 (sin π/3) = π/3, is sin-1 (sin 5π/6) = 5π/6? Explain your answer.

A: It is given that sin-1sinπ3=π3.

Q: Rewrite cos x + 3 in terms of sin(x) and cos(x). COS

A:

Q: Consider the given equation. cos(x) sec(x) sin(x) csc(x) – sin(x) (a) Verify algebraically that the…

A:

Q: Let sinA=-4/5 with A in QIII and cosB=-3/5 with B in QII. Anwer Exactly. Find sin(A-B), cos(A-B),…

A: Given,

Q: Verify the identity sin t - cos 2t = (2 sin t - 1)(sin t + 1).

A: sin t - cos 2t=(2sin t-1)(sin t +1)Formulascos 2t= 1-2sin2t

Q: Verify the identity: sin (3π/2 - x) = -cos x

A: To prove  sin (3π/2 - x) = -cos x

Q: rewrite cos(x+4pi/3) in terms of sin(x) and cos(x)

A: