Q2) By using the addition formula derive the identity of the function sin (x -)

Q: 2. LOshx-Sin hx1 2. Co

A: We use hyperbolic Trigonometry identies

Q: Find all values of x such that sin 2x = sin x and 0 <x< 2m.

A: sin 2x=sinx⇒sin 2x-sin x=0⇒2 sin x cos x -sin x=0⇒sin x2 cos x-1=0⇒sin x=0  or  2 cos x-1=0 sin…

Q: Verify the identity tanh2 x + sech2 x = 1

A:

Q: Use the addition formulas to derive the identities

A: We will use cos(A-B)=cosAcosB+sinAsinB formula with A=x and B=π/2

Q: Express sin S as a fraction in simplest terms.

A: Topic:- trigonometry and geometry

Q: if x+1/x=2,find sin-1x

A: Given,

Q: If f(x) = 7 sin-(*), then f'(2) - =

A: dsin-1xdx = 11-x2 dxndx=n.xn-1

Q: 1 o. = 0. Show that lim x² sin -| *

A: Use the property that -1≤siny≤1. Take y=1x, then -1≤sin1x≤1

Q: is: The number of zeros of sin(-) is: `z-1

A: If y=f(z), then the variable z is called the input of the function, and y is called the output of…

Q: find maclurin formula in the fourth degree for f(x)=secx

A: To write the maclurin formula in the fourth degree

Q: What is the value of * cosx + sin2x + 1 lim x² – 7²

A: what is the value oflimx→π cosx+sin2x+1x2-π2

Q: By using the relationship between the hyperbolic sine function and its Ssinh- (x)] = V. inverse,…

A:

Q: Q3) Use the addition formulas to derive the identity of (cos (x --): sin x ) %3D

A:

Q: 2 cos(5x) – 5 x² – 2 sin(3x) – x2 – 3x - lim - - (Write your answer in the given box)

A:

Q: Evaluate ∫sin2 x cos4 x dx.

A:

Q: Find an alternative form in terms of x for each of cos(sin- 1 x) and tan(sin- 1 x).

A: Let us make a triangle with opposite = x and hypotenuse=1 , because sin theta= opposite/hypotenuse…

Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: cos 2x +1 Prove that sin 2x

A:

Q: What is the value of cosx + sin2x + 1 lim x2 – 72

A:

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: Use an identity to solve the equation tan x - sec x = 1 on the interval [0, 2π).

A: The given equation is tanx-secx=1.

Q: If f(x) = 7 tan-(2 sin(4)), f'(2) =|

A:

Q: If f(x) = 2 sin- (24), then f'(x) =

A:

Q: Use th Start! 1- cos 2x

A: Given:1-cos2x/cos2x To simplify we use some trigonometric properties

Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

A:

Q: If tanh(x)=5/13, what is the sinh(x)?

A: Answer is sinhx=5/12. Explanation is given below..

Q: e in Q2, find Sin (2e) with 6 If csce -6,

A:

Q: Complete the statements.

A: Given Our aim is to complete the sentence

Q: * Find the value of Tx³ + 2. lim [sin (- x3+1] -1 O

A:

Q: If f(x) = 2 tan-'(8 sin(4x)), f'(x) =

A:

Q: If f(x) = 3 tan-'(3 sin(3x)), f'(æ) =

A: The given function f(x)=3tan-13 sin(3x)

Q: If f(x) = 2 tan '(5 sin(3r)), f'(x)-

A:

Q: 6. Use the identities to find cscx and cotx if secx =7 and sinx < 0. Show all work.

A: Solve question number 6 as asked by the user .

Q: 1 If f(x) = 8 tan¯¹(8 sin(2x)), f'(x) =

A: Differentiate

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

A: To prove  sin (3π/2 - x) = -cos x

Q: Write the expression as an algebraic expression in x for x > 0. sec sin-1 x2 + 36

A:

Q: Prove the identity. ex(1- sin'x) = So cosx | %3D

A: Prove the identity- Secx(1 - sin2x) = cosx. We know that : sin2x + cos2x = 1 Here i attached…

Q: If f(x) 5 tan (7 sin(2r)), f'(x) =

A:

Q: 05 of the ac 42. Use the identity sin 2x = 2 sin x cos x to find the derivative of sin 2.x. Then use…

A: Find the derivative sin2x

Q: Is f(x)=cos^2(x)-sin^2(x) even, odd, both, or neither?

A: Given,           f(x)=cos2(x)-sin2(x)

Q: Find cos(2x) Given that sinx= 4/5 and 0&lt;x≤ pi/2

A:

Q: lim,-o-cos(2.x) →0°sin²(3x) Q6- Evaluate:

A:

Q: If f(x) 3 tan-'(3 sin(3x)), f'(z) =

A:

Q: A func tion f is given. sin 4x f(x) = 2.x Is f even, odd, or neither?

A: We have to find type of function if fx=sin4x2x We know that  if we replace x with -x and after…

Q: If f (x) = - sin(x), then f (10) (x) is equal to = - sin(x), thenf (10) (x) is equal to A - sin(x) B…

A:

Q: If f(x) = 7 sin - (2²), then f' (æ) =

A: We know , d/dx (arcsin(x))= 1/√(1-x²)

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.