Group (A) tane + sece -1 1+ sin® Q1/, Prove that Tane - sec® + 1 cose Q2/Prove that cos 17° + sin17° = tan62° cos17° – sin17° Q3/ Evaluate lim → /2 (1+ cosr)3 secx Q4/Find the length of the perpendicular from (2,-3) to the line 2x - y + 9 = 0 ?

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: 2 cos(4x) – 4x2 – 2 lim - I→0 sin(2x)- x2 - 2x

A: We have to evaluate the limit limx→0 2 cos(4x) - 4x2 - 2sin(2x) - x2 - 2x

Q: 2- i) By using L'Hopital Rule, find sinx lim x-0 e3x – 1 ii) Given that a = sin-1 , find ,csca

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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: 3x²+x d (sin-()+sec='(x) (1) Compute lim cot-1(3x+*+1) (ii) Find- X+00 3x2-7 dx tan-1x+tan-1

A: i).…

Q: 1) tane = 2.6 2) cos0 = -0.65 3) csc(-0) = - 2 tan(-0) = cos(-0) = csce = 6. 4) sec(-0) = 3 &…

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Q: prove tany csc3-tanX =cos x CSCX Sinx tanx tcosX-

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Q: 1- sin0 lim а) 1+ cos 20 2

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Q: 2 1. sin 0 == and sec 0 > 0 2. sece = - and tan 0 > 0 3

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Q: Plot y = B sin(Aπx) cos(x) with a solid line over the interval 0 < x < 3 with the vertical axis set…

A: close allclear allformatclc A = 21;B = 5;C = 3;y1 = @(x) B * sin(A*pi*x) .* cos(x);y2 = @(x) B *…

Q: sin- In2 4+ tan-'cos- dx 2 2 I+ cos2* 4+ tan-'cos- In2 4+ tan-'cos- dx 2 2sin- 2 A 1+ cos 4+ tan…

A: To evaluate: ∫sin x2 ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

Q: If tan x = 3, cos x > 0, , then - sin 2x cos 2x tan 2x %3D

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Q: lim as x approches 0 of cos(6theta)-1/sin(7theta)

A: Given: fθ=limθ→0cos6θ-1sin7θ Apply limit by substituting θ=0 in the above expression.…

Q: Find all points (if any) of horizontal and vertical tangency to the curve                 x = 4 cos2…

A: Given: x = 4 cos2 θ,  and  y = 2 sin θ  To find: All points of horizontal and vertical tangency to…

Q: 1-cos 2x lim x2 sec x-tan x lim X→0 X→- 2 x- 2 x2 +sin 3x lim 2x+tan 2x . х-0

A: We are solving first question for you. If you want solution for any other question than please…

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: Which cosine function has maximum of 2, a minimum of -2, and a period of 277 3 Oy= 3 cos 20 20 Oy=2…

A: Given: The maximum value of cosine function is 2 and minimum value is -2 and the period is 2π3, To…

Q: lim cos2x-1/sinx x-> 0

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Q: cos(-x)+sin(x=x) Q4 prove that sinx 2

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Q: sin°(,² – 4) (x+2) tan(x+ 2 limy→-2

A: We have to solve

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

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Q: 2, 2. prove that tan¯0+cot-0+2= sec´0cosec´0

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Q: 12. etan 2x sec² 2x dx 13. Jdx/(x²-4) 14. (2x¹-x²) dx / (2x² + 1) 15. f (sec²x) dx/(√(1-4 tan² x))…

A: Given

Q: 1-cos(2x) - Evaluate: a- lim,-0 sin²(3x) tan x-sin x b- lim sin3x

A: According to L'hopitals rule,limx→af(x)g(x)= limx→af'(x)g'(x)iff(x)g(x)= 00or ∞∞. If there is any…

Q: Prove: sec 0 + tan(-0) cot 0 - cos (0) = sec 0 tan 0

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Q: 2 1-tan ² x 2 1+ tan² x 2 = cos²x - sin² x

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Q: Example 2: find ỹ,y=sin-1 Vx.sec-1 (sin x) Example 1: find ỹ,y=tan-1(x². sin x) Example 3: prove…

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Q: √3 csc x − 2 = 0  tan 3x(tan x − 1)  sin2 x = 3 cos2 x

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Q: 3.1 Find and classify singularities of sin) 3 -

A: Please check step 2 for the solution.

Q: sin 2x+cos2x+1 1- Prove cot x sin 2x-cos 2x+1

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Q: Find the points on the cardioid r = sin(2θ) where the tangent line is horizontal. Draw.

A: We have to draw the cardioid r=sin(2 theta)  And find the point where the tangent line is…

Q: A-prove: (chose 4 only) 1-sinx 1. lim 1+cos2x

A: Q-1,1) Given- limx→π21-sinx1+cos2x=14 To Prove- The above expression.

Q: Prove the identity.   (1-tanx)^2=sec^2x-2tanx.

A: We have to prove the identity(1-tanx)2= Sec2x - 2 tanx

Q: Lim -> 0 Sin3ycot5y/ycot4y

A: limy→0       sin 3y .cot 5yycot4y   =limy→0    sin3y tan4yy tan5y 00farm…

Q: solve using L'Hopital's Rule 7. Lim    1/(tan-1)2  -  1/x2    x->0

A: Given the limit as : limx→0 1tan-12-1x2 We need to find the limit by using L' Hopital's Rule. Let's…

Q: lim x->-7  (-x-7)/(4-√(9-x)) lim x->-infinity (√6x^2 - 2x)/(x+8) lim x->0 (7x cos x + sin 5x)/3x

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Q: sin 2x+cos2x+1 1- Prove cot x %3D sin 2x-cos 2x+1

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Q: 1+ sin 0 1- sin 6 Prove that (tan 0+ sec 0)2 Do NOT start your proof by assuming the conclusion.

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Q: V3 1) tan 3 cos¯1 –1 -1 2) cos-1 | 3) sin- 0 4) tan-' (-V3) 5) tan- 6) sin- 7) cos 2 8) tan- –1

A: tan-133

Q: [((1-tan^2(x))/sec^2(x)]= cos(2x)

A: To prove that  [((1-tan^2(x))/sec^2(x)]= cos(2x)

Q: 1-cos(2x) limx→0 sin² (3x) tan x-sin x lim - Evaluate: а- b- x→0 sin³x

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Q: 1-cos(2x) tan x-sin x Q6- Evaluate: a- limx-0 b- lim x-0 sin (3x) sin³x

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Q: Prove that: sec (0) +tan (0) cot (0)-cos (0) -=sec (0) tan (0)

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Q: Find exact function values for: a. sin(α/2) b. cos(α/2) c. tan (α/2) cosα = 12/13, (3π)/2 < α <…

A: The given trigonometric ratio is cosα=1213 ,where3π2&lt;α&lt;2π (a) To find the value of sinα2…

Q: tan(3z) lim 5z z-0 sin(n)(1-cos(h)) lim h-0 sin(h)(1-cos(h) lim h-0 h3

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Q: 3 8. y = sec Зx) 9sec (2 – 3x)tan´(2 – 3x) B. - 9sec (2 - 3x) tan tan (2 3 С. 9 sec' (2 — 3х) tan…

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Q: sin- In2| 4+ tan¬'cos- dx 2 2 1+ cos- |4+ tan-'cos= 2 2sin- In2| 4+ tan-'cos- |dx 2 2 A 1+ cos2…

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Q: () - VE ()- 1+cos 0 1-cos 0 Show that cos and sin (: using de Moivre's Theorem.

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Q: 1-cos 2X lim x→0 x2 sec x-tan x lim X→- X- 2 x2+sin 3x lim r20 2x+tan 2x

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Q: 2. Prove sec?x + tanx secx 1- sin x

A: cos^2 x = 1 - sin^2 x sec x = 1/(cos x) tan x = sin x/cos x