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: if cos(X+pi/6)+sin(x-pi/3)=A, then the number A =

A:

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

A:

Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

A:

Q: Derive the Product-to-Sum formula sin a cos B = [sin (a+B) + sin (a-B)]. ..... First, rewrite the…

A:

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

A:

Q: Use an identity to solve the equation cos 2x = cos x on the interval [0, 2π).

A: Given:cos2x=cosx on the interval [0,2π)Formula:cos2x=cos2x-sin2xsin2x=1-cos2x

Q: 1/2 sin e cos (cos a cosec 0) de TC (1-cos a).

A: Note that we have to show that the integral value is  π2(1 - cosα).

Q: (1) Find the exact values, without using a calculator, of sin (2r), cos (2r) and tan(2r) if tan (r)…

A:

Q: expand the formula for sin(A+B)

A:

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

A: To prove  sin (3π/2 - x) = -cos x

Q: 2/5 If cos a = and sin a < 0, find the exact value of cos (a +) Show the formulas you are using.

A: The trigonometric function value is given by cosα = 255 and sinα&lt;0 To evaluate : The value of…