x+ cos X Find the derivative of tan x . O A) tan x+ tan xsin x+ xsec x+secx tan? x tan x(1+sin x) O B) (x+cos.x)sec x O C) tan x- tan x sin x-x secx-secx tan x O D) 1+ sin x secx O E) None.

Q: ind the slope of the tangent line to the curve 4 sin(x) + 5 cos(y) − 5sin(x)cos(y) + x = 3π at the…

A: To find the slope of the tangent line of 4sin x+5cos y-5sin xcos y+x=3π, differentiate it and…

Q: 5) Prove that tan(x) + cot(x) = [sec(x)][csc(x)]

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Q: y = tan(x sin x) O (x + sin x) sec² (x sin x) O (x cos x + sin x) sec² (x sin x) O (x + sin x) sec(x…

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Q: If f(x) = cos x – 7 tan æ, then f'(z) -sin( x ) – 7 sec²(x) = f'(2) =

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Q: sec z 47. tan z tan z

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Q: Find the minimum value of ∣sin x + cos x + tan x + cot x + sec x + csc x∣ for real numbers x.

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Q: For (cos(2x) – sin cos(x) – sin(x) - sin(2x) cos (2x)) +C. What is F (x)? A sin cos³ (x) – cos(x)…

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Q: tan"x jun's de - | tan"-x dx (n 1) n- 1 tan x sec" r sec x dx (n 1) n- 1

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Q: Prove that sec x dx = In sec x+ tan x +C.

A: Here the question is solving by using u-subsitution method.

Q: 2 Using the relation 2 (1 cosx) x, V x € (0, - · 4)

A: A relation is given by, 21-cosx < x2, where x≠0. The objective is to use the given relation to…

Q: Find all points (if any) of horizontal and vertical tangency to the curve on the given interval

A: Given Data The first equation is x=cos θ+ θ sin θ. The second equation is y=sin θ- θ cos θ.…

Q: Verify the identity. tan(x) cos(x) csc(x)(1 + sec(x)) tan(x) tan(x) 1 cos(x) IN 1. cos(x) 1 + cos(x)…

A: The given question can be solved as shown in step2.

Q: Prove that: 1) csc 0 + tan 0 . sec 0 csc 0.sce20 1-cos" x 2) sin x .cos x tan x 3) 3 cos' x-sia x+1…

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Q: 1. sin (5x + ) sin ( x + T /2) %3D 2. tan (3x – T/2 ) = cot 2x 3. COs (x + п /2) sin ( T /2 – 2x )…

A: Given that three trigonometry equation  To find fundamental solution of the question

Q: Q2/ Find f (x) : 1- f(x) = 4 cos x + 2 sin x 2- f(x) = cos x - x csc x 3- f(x) %3D %3D cot x 1+cscx…

A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

Q: Prove: sin x tan x+cos xcot x+2 sin x cos x = tan x+ cot x + cos²

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Q: 1+ sin x 1- sin x 21. 1- sin x 4 tan x secx 1+ sin x sin (x + y) sin (x - y) tan x + tan y 22. %3D…

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Q: 4. Prove the identity: sin x + tan x = tan x cos x + 1 (sinx¥, sin x COS X LS = cosx + 1 V sin x cos…

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Q: Differentiate. f(x) = 4 sin(x) − 7 cos(x)

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Q: Verify. a. (2 tan x ) / (1 + tan2 x) = sin(2x) b.  1 / (1 − sin θ) + 1 / (1 + sin θ) = 2 sec2 θ c. 1…

A: Part a)Given:

Q: 1 1 Prove -2 secx tan x 1+ sin x 1- sin x

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Q: tan°(x) sec²(x) dx = 1/7tan^7(x)+1/9tan^9(x) %3D

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Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: Evaluate / 5 sec2 *dx tan(x) 05 In(|tan(x)|) + C Oln(tanx) + C 05 In(x) + C 05 tan(x) + C

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Q: Let f(x)= ln(e^x +2x) -2 Find equation for tan line at x=0

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Q: sin(-æ) = - %3D V2 tan(x) = – %3D cos(x) csc(x) cot(x)

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Q: What is the value of 4 (sin x tan dx X)? a) sin x + tan x sec x b) cos x + tan x sec x C) sin x +…

A: ddxsinxtanx= cosxtanx+sinxsec2x=sinx+tanxsecx

Q: D,(6 tan x) 6 sec² x sec² x (c) D,(In |6 tan x|) %3D 6 tan x 6 tan x tan x

A: Consider the given function as Dxln6tanx

Q: Proof 2: 14 sin x dx tan xdx = /6 COs x 1 -= sec x dv = sin xdx cos x du = sec x tan xdx v =-cos x…

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Q: limit x to infinity (1+sin(3/x))^x

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Q: Verify the identity. tan(0) sin(0) + cos(8) = sec(0) tan(0) sin(0) + cos(0) : sin(0) + cos(0) cos(0)…

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Q: 1. f(x)= xsin x 2. f(x) = x?cos 2 x 3. f(x) = tan x – sec x sin x 4. f(x) =

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Q: Prove: 0 =- 1 Proof 1: sin x tan xdx = [ cos x 1 u = cos x dv = sin xdx sec x du = sec x tan xdx…

A: Solution is given below:

Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

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Q: 1. cos x 1 - sin x = sec x + tan x

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Q: Verify the identity tan(x) Cos(x) csc(x) (1 sec(x)) 1 1cos(x) 1cos(x) tan(x) cos(x) tan(x) 1 -…

A: Given identity to be verified is

Q: If f(x)=tan x, then show that f(x+y)-f(x) = sec^2x tany/ 1-tanxtany

A: The detailed solution is given below Thank you

Q: 4sin'x – 1 1. 2sinx + 1 = 2sinx – 1 sin'x – 2sinx + 1 2. = sinx – 1 sinx – 1 3. ( sinx - cos x)(sinx…

A: Simply use the basic concepts of algebra and simplify the each one.

Q: Prove (sec x sec y + tan x tan y) - (sec x tan y + tan x sec y) = 1

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Q: a sin (cos X) b cos (cos x) c sin (sin x) d cos (sin x) a By expressingy = x in the form y = sin…

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Q: Prove that 1+ cos x + V1-cos x X +,0<x<" 4 tan %3D 1+ cos x -V1- cos x 2

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Q: 5- Prove that a) tan x (csc x – sin x) = cos x b) 1+ secʻx sin´x = sec´x x = sec¯x

A: (a) Consider LHS and simplify as follows. tan xcsc x-sin x=sin xcos x1sin x-sin x…

Q: Differentiate. 6 - sec x y = tan x -sec(x) tan(x) - tan(x) – 6 – sec(x) - sec2 (x) y' = tan ?(x)

A: We know,d(u(x)v(x))dx = v(x) . du(x)dx- u(x) . dv(x)dxv2(x)

Q: Prove (sec x sec y + tan x tan y) - (sec x tan y + tan x sec y) 1

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Q: tan x sec xdx = (sec x) * - (sec 2)* +c 10 음(tan x) 을(tan z), +c 10 None (tanx) + (tan x) +c 금 (sec…

A: Given:⇒∫sec4x*tan(x)3dxWe know that sec2x=tan2x+1⇒∫sec2x(tan73x+tan(x)3 dxSubstitute u=tan(x) →…

Q: 10. f cos*x sin x dx 11. (sec² 3x) dx / (tan 3x) 12. Setan 2x sec² 2x dx

A: Topic:- integration  Note:- as per our guideline if more than three subparts posted than only first…

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

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Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

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Q: 1-tan x 1+ tan x sec x-CsC X a. sin x + cos x sin x COS X b. sin x +cosX sin x + cos X C. sin x- cos…

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