Calculus Show that the difference quotient for f(x) = sin x is given by f(x + h) – f(x) sin (x + h) – sin x h h sin h = cos x. h 1 - cos h sin x • h

Q: Prove the identity. tan(x) − tan(y) 1 − tan(x) tan(y) =  sin(x − y) cos(x + y)

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Q: sin x 14) Simplify: sec(x) tan x A) 1 C) sec² x 7n B) tan(x) D) sin(x)

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Q: sec x- sin xtan x= cos

A: see 2nd step

Q: Letr> 2. Show that sin² r - sin² 2 r-2 < 2. Justify your answer. Hint: Apply the Mean Value Theorem…

A: Let r&gt;2.   To Show: sin2 r-sin2 2r-2&lt;2.

Q: sin sin 3x = 2 co 4 sin x cos x - 4 sin x cos x X COS X vith the left-hand side, use a Sum-to- sin…

A: Here we have to verify the idnetity,  sin5x+sin3x4sinxcos3x-4sin3xcosx=2cosx

Q: •sin ² (x/2) = = (tan x sin x)/ 2tan x = sin ² (x/2) •tan x - cot x = - 2cot 2x •sin ² (x/2) = (sin…

A: 3) sin2x2=sinx tanx22=sin2x2 4) sin2x=2cos2(x/2)1-cosx=sin2x 5) 2sinx-sin2x/(2sinx+sin2x)=tan2x/2

Q: VERIFY THE IDENTITIES

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Q: sin x cOs x 1 – sin x 2sin x 2 cos x 3 cos x -1

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Q: sin(2x) cos(2x) Prove sec(x) sin(x) cos(x)

A: Trigonometry

Q: sin x 2. Find f'(x) if f(x) = 1 - cos x %3D 1 3. Simplify your result in (2) to show that f'(x) %3D…

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Q: Verify the identity.

A: Use the trigonometric identities sinA+sinB=2sinA+B2cosA-B2 and cosA+cosB=2cosA+B2cosA-B2 to simplify…

Q: 1/sin(x)/cos (x)+cos (x)/1+sin(x)=4 Prove

A: For x= pi/3

Q: sin (In (x))x

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Q: Express the function in the form f∘g. F(x)=cos2x

A: Given : Fx = cos2x

Q: sec x sin x sin.x Cosx 1 – cosx sin x sin.x 1- cos.x

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Q: Verify the identity:

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Q: sin 2 x + sin x + cos 2 x - 1 = _______ tan x cot x sin x cos x

A: We can solve it as below.

Q: sin x 1+cos x 1-cos x sin x

A: Let's prove that given trigonometric formula.

Q: (sin x + cos x) sin'x- cosx sin'x- cos'x cos-r COS X (sin x – cos x)2

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Q: snip

A: fx=cosx

Q: sin Show that the set of functions. 3πX 5TX 2L 2L TCX 2L sin sin is orthogonal over (0, L).

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Q: Lim 2-2 cosx - xIn (1+x). x sin'x

A: We apply L hospital rule to find the limt. See 2nd,3rd and 4th step.

Q: cos2x – sin2.x cos2x - dx = -F(x)+C. What is F(x)? 3 For cosx – sinx 1 (A (sinx – cosx osx) - B sinx…

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Q: Verify the identity. 1 + sin(x) 1 - sin(x) 1- sin(x) 1 + sin(x) 4 tan(x) sec(x)

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Q: cos2x – sin2x cos2x For dr3-F(x) +C. What is F(x)? cosr - sinr 3 2 cos'x+ cosx + A sinx + -sin'x B…

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Q: sin(x ²–4) -4) lim x+2) tan (x+2) x→-2

A: Rearrange the expression than Apply the limit and simplify.

Q: sin x+ tan x+cos´ x

A: We have to simplify  For this we will use the trigonometric identity formula.

Q: QI Find f'(x) for 1+ sec1(x) 1- csc-1(x) csc (x) + sec '(x) V(-1)(csc 1(x) - 1)* csc (x) + sec '(x)…

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Q: proof : cos4x/sin2x+cos2x=cos2x-sin2x

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Q: Verify the following identity:

A: We have to prove the following trigonometric identity: sin4x2-cos4x2sin4x2cos4x2=-16cos xsin4 x

Q: f"(x) = cosx – tan x. f'(x) If f(x)=enx, show that = cos x-

A: The given problem is to show the following proof of identity. Given f(x) = esin(x)  we have to show…

Q: f(x)=2cos^2 x-1 , 1-2sin^2 x , cos^2 x-sin^2 x and cos2x Make a comparison of the four expressions

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Q: Af function is said to have a "fixed point" if there is some point p where f (p) = p. Show that the…

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Q: cos(x+π6)+sin(x−π3)=______

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Q: sin^2 x + sin x cos x over cos x − 2 cos^3 x

A: This question is based on Trigonometric Formulas to simplify question.

Q: cos2x – sin2x cos2x For -dr=-F(x)+C What is F(x)? Cosx - sinx 2 3 2 sinx + -cosx+ cosx + - sin³x 3 3…

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Q: cos2r – sin2x cos2x For -dr=-F(x)+C What is F(x)? cosx – sinx 3 2 sinx + -cos'x+ cosx+ =sin³x 3 3 2…

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Q: (sec x + tan x)2 = (1 + sin x)/ (1 - sin x)

A: Given :(secx+tanx)2=1+sinx1-sinx

Q: 2 sin x tan x - tan x = 1 - 2 sin x

A: Answer and explanation is given below

Q: sec2 x. Let y = tan x. PROVE that y'

A: Topic = Derivative

Q: sin 3x 39.lim tan 6t 41. lim 50 sin 21

A: We will use the l'hospital rule to fine the limit of 39.  To fine limit 41. We will use the basic…

Q: cos2x- sin2x cos2x For dr=-F(x)+C What is F(x)? COSX sinx 1. (sinx COSX O (cscx x – secx) ³ CSC)…

A: We have to find F(x) by indefinite integral

Q: cos2x – sin2x cos2x -dr=-F(x)+c•\ For + C: What is F(x)? cosx - sinx 3 1 (sinx – cosx) O (cscx –…

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Q: How is domain of the function f (x) = sin x restricted so that its inverse function exists? Drag a…

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Q: 4. lim sin2ß B-0 sin3ß

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Q: 93. Proof Prove each differentiation rule. (a) [cot x] = -csc² x dx d (b) [sec x] =sec x tan x - dx…

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Q: Verify the identity algebraically. Use the table feature of a gaphing utility to ch 3 cos(x) 1-…

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Q: sin x cos x tan x = 1 – cos² x -

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Q: sin x + 2 sin x +1 1+ sin x cos COS X 1 Sin X

A: We have to verify: sin2 x+2 sin x+1cos2 x=1+sin x1-sin x

Q: sin x 25) lim x→0 5x 3(1 – cos x) 26) lim sin x (1 – cos x) 27) lim 2x2

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