sin(x) cos(x) Consider the function f(x) = tan(x), and remember that tan(x) = (a) What is the domain of f? OA. All real numbers except +, ±,+,... OR. All real numbers OB. All real numbers except zero OC. All real numbers except 0, ±m, ±2ñ, ±3™,... OD. All positive real numbers. OE. None of these (b) Andre computes f'(x) using the quotient rule. Which of the following is a possible correct answer? cos(x) cos(x) + sin(x) sin(x) cos (x) cos(x) cos(x) – sin(x) sin(x) cos (x) A. f'(x) OB. f'(x) = Oc. f'(2) = cos(x) sin(x) + sin(x) cos(x) cos²(x) cos(x) sin(x) – sin(x) cos(x) cos (x) sin(x) sin(x) – cos(x) cos(x) cos?(x) OD. f'(x) OE. f'(x) = OF. None of these (c) Berenice simplifies Andre's correct answer using the Fundamental Trigonometric Identity. Which of the following is a correct answer? 1 OA. f'(x) = cos?(x) cos(2æ) sin(2a) cos²(x) 2 cos(x) sin(a) cos (x) cos(x) – sin(x) cos (x) sin(x) – cos(x) cos (x) OB. f'(x) = Oc. f'(x) = Op. f'(x) OE. f'(x) OF. None of these (d) Corey simplifies Berenice's correct answer using another trigonometric Identity. Which of the following is a correct answer? OA. f'(x) = sec2(x) OB. f'(x) = csc²(x) OC. f'(x) = cot(x) OD. f'(æ) = cot2(x) OE. f'(x) = csc(x) OF. f'(x) = sec(x) OG. None of these (e) For what values of x is f'(x) defined? OA. All real numbers except + ,±,±, ... OR. All real numbers OB. All real numbers except zero OC. All real numbers except 0, ±7, ±27, ±3T,... OD. All positive real numbers. OE. None of these

Q: EXamples about Damain and Range Sinx +1

A:

Q: Which of the following functions is/are TRUE? A sinh(-x) = -sinhx B cosh(-x) = coshx tanh(-x) = -…

A: topic- hyperbolic functions we know that sinh(-x)=-sinh(x) cosh(-x)=cosh(x) tanh(-x)=-tanh(x)

Q: Solve: 5+ln(4x - 7) = 8

A: solve :  5+ln(4x-7)=8 evaluate : sinπ3

Q: Use trigonometric identities to simplify the expression. SEC(X) / CSC(X) OR  sec(x) *over* csc(x)

A:

Q: sin(x-y) sin(x+y) tan x-tan y tan x+tan y ||

A: The given statement is: sin(x-y)sin(x+y)=tan x-tan ytan x+tan y

Q: 11) State what the inverse functions of the following. Give the domain and the range of the original…

A: Ti find the invesre of the trignometric functions and find their domain and range.

Q: What are the domains and ranges of the following functions? Function Domain (Choose one) y= sec x…

A:

Q: Which inverse trig functions have restricted values from 0 to n? You must choose all correct to…

A: the range is all the values the inverse function of Trigo can take.

Q: Let x be a real number between 9 and 11. Provide an expression for sin(cos-(x - 10)) (in terms of x)…

A:

Q: a-X Tan" 1+ ax Differentiate

A:

Q: cot(-0)+tan(0-) TT = 1 – 2sin² (0) tan(-0)+cot(-0) |

A: The given statement is: cotπ2-θ+tanθ-π2tan(-θ)+cot(-θ)=1-2sin2θ

Q: What is the expression that completes the identity tan(x)+cot(x)

A:

Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

A: LCM (least common multiple)  tan x = sin x / cos x cot x = cos x/ sin x  Also, tan x * cot x = 1

Q: Show that for all real x sin x 1 sin²x x + sin³ x x + 2 sin x 2 + sin x

A: We need to show that, sin x  - 12 sin2 x + 14 sin3 x - 18 sin4 x + ...... = 2 sinx2 + sinx Consider…

Q: which is f-1 (x)? f(x)= 1/5x + 3/5

A: Given, fx=15x+35 We have to find f-1x.

Q: Simplify the following as a product of trigonometric functions with no powers. Write the functions…

A: Given that, Now simplify the following trigonometric function:

Q: 1/ 1-sin t + 1/ 1+sin t   Use trignometric identites to write the expression in terms of a single…

A:

Q: Prove identity (1+ a) (1 – cos a) = tan? cos æ) sec x x cos x

A: