2. Verify that the Mean Value Theorem (MVT) applies to the function f(z) = sin² z- on the interval , COS I 37 and find all the values satisfying the conclusion of MVT.

Q: Prove the following  (sinx)(secx)(cotx)= 1

A:

Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: Show that sin-1 v + cos-1 v = π/2 .

A: Given: sin-1 v+cos-1 v=π2

Q: Determine the two roots of sin x + 3cosx - 2 = 0 that lie in the interval (-2, 2). Use the secant…

A: Method by solving trigonometric equation

Q: Prove: sin (2 cosx) = 2x1-x

A:

Q: Show that sin(sin-1 v + cos-1 v) = 1.

A: sinsin-1v+cos-1v=1

Q: Find the exact values of x in the interval [0, 3pie] that satisfy the equation sinx= -1/2

A:

Q: Find the first and second derivatives of r = [3 cos 2t, 3 sin 2t , 4t].

A:

Q: Evaluate: sin-l z = - cos™(-3+j5) O -5.074-j2.957 -5.074-j2.957 D-5.074+j2.957 5.074+j2.957

A:

Q: Show that tan-1 ( 1/v ) = π/2 - tan-1 v, if v > 0.

A: To prove tan-11v=π2-tan-1v, let  x=tan-1v then tan x=v1tan x=1v Since  tanx=1cotxcotx=1v ⋯ (1)

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: 3. Prove the identity tan * COS v t CSC x Sinx=2sinx

A: Prove the identity

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative