tan (0) +1 1) sec(e) = sec(0) cos(@) +1 2) tan (0) cos(@) sec(@)-1

Q: 7x cos х -7x - lim [sin(-2x)sin(5x)sin(7x)] 2x3cos(x) lim 5x2 х>0

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Q: cOs x tan x 28) lim sin 3x 29) lim x→0 2x x3 + 2x2 + x 30) lim x→-1 x4 + x3 + 2x + 2 x3 – 2x2 + 4x –…

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Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

Q: 2 cos(4x) – 4x? – 2 - - 8. lim x→0 sin(2x) – x2 – 2x -

A: Topic = Limits

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

A:

Q: c) cos x tan x = sin x tanx %3D (Usx.SinzL (os x Sinc sinx cot x + = csc x - CSC X 1+cos x (e Sinzx…

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Q: 4 cos 4 cos dx () х3 sin3 4 - у4 - х dx

A: (1) using integration by substitution∫4 cos1x2x3 sin31x2 dxlet   sin1x2=udifferentiate both…

Q: 5. tan (x)dx 1 -dx cos² (x) sin () 6.

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Q: cos x-2 cos 3x + cos 5x b. cos x +2 cos 3x + cos 5x :-tan x. %3D

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Q: cos 2x–1 lim COS х— 1 cos x-1

A: limx→0cos 2x-1cosx-1

Q: 6. cos x(csc x secx) secx) cotx

A:

Q: 1-cos 3x +C dx 1+ cos 3x 3sin 3x

A:

Q: 2 cos(8x) – 8 x² – 2 lim - sin(3x) — 2? — За

A: Here we apply l Hopital's rule.

Q: =) lim cos 3x sec 7x Xー

A: 1) a) The given function is, limx→π2cos 3x sec 7x. limx→π2cos 3x sec 7x=00 Rewrite the given…

Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

Q: sin(3x) cos(6x) – cos(3x) sin(6x) = -0.6 X =

A: There is trigonometric identity sinA-B= sinAcosB-cosAsinB

Q: 2dx 2 2 cos x√ 4tanx - tan x S-

A:

Q: FIN 2 dx

A: Note:- In given problem, according to written way sin2x is multiplied by 3x+1. If you want solution…

Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral.

Q: cos 2x - 2 sin x- cosʻx=-3

A: Consider cos 2x-2 sin x-cos2 x=-3  . . . . . (1) We have cos 2x=2 cos2 x-1 . . . .  . . (2)

Q: 5. 4 (secx-1)(sec² x+secx+1) Sª cos² 2x-2 cos 2x+1 -dx

A: Indefinite integral is the process through which one can determine the function which on…

Q: 1. f(cos 3x - x²) (sin 3x- x³)5 dx 2. f cos² x (tan x) (sec² x − 1) dx 3. f tan x (sec² x - 1)(sec²…

A:

Q: tan20 21-25. Verify = sec?e – sec 0 cose + 1

A: To verify: That tan2θcosθ+1=sec2θ-secθ. Formula used: Trigonometry identity: tanθ=sin θcos θ…

Q: cscxdx 5+ cos²x sin²x

A: Evaluate: I=∫csc2x5+cos2xsin2xdx We know that, cos xsin x=cot x Then, we have I=∫csc2x5+cot2xdx

Q: 11) cos x csc X tan x - 1 11) 12) cos2x - sin2x = 1 - 2 sin²x 12)

A:

Q: lim * In(sec(2x)) x→0 (sin(3x))³

A: To find the limit.

Q: cos x sin x = csc 2x cos 3x sec 2x

A:

Q: 1-Cos 2x 1+ Cos 2x ix) tan x=

A: Prove :

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: 7- I = [sec(2x) tan(2.x)dx cos(2x) 8- I = dx 4-sin (2x) csc (In(x)) 9. I: dx

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Q: 1. sin x sin 2x + cos x cos 2x = COS X

A:

Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

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Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

A:

Q: (5) f(x) = cos (5 - 2x) (7) f(x): = cos (√x³ + 1) (9) f(x) = cot (x5) (6) f(x) = cos (4x7 + 3) (8)…

A: Note: As per company guidelines we solve only first three subparts when multiple parts question…

Q: 1+ cosx + sinx sinx 1+cos X 2sec x 2csc x 2csc 2x 2sec 2x

A:

Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

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Q: 2 sin'x - cos x sin'x - (1 - sin'x) in*s) Rule ? %3D sin°x - 1 + sin´x Rule ? %3D = 2 sinx - 1 Rule…

A:

Q: 1 1. sec-1 x = cos-1 = cos

A: we have to show that the given relation.

Q: 1. f(x) = cos 3x2. y = - tan 12x3. f(x) = sec x? 4. y = sin(2x² + 5)5. y = 12 csc6. f(x) = sin(x +…

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Q: 1. Lim 2×ー2xーメ+1 x-x3- 2x + 2 3. Lim メ→。 |- Cos X X-1 Sin 2x 2. Lim csc ax Csc 2x 4. Lim 7X 2x+5 x-…

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Q: y = sin(2x) sin(x) + cos ( 2x) cos (x) COS %3D

A: Using the formula of cos(A-B)=cosAcosB+sinAsinB. Explanation is given below..

Q: y = cos (tan (3x)) A. -9cos? (tan (3x))sin (tan (3x)) sec (x) B. -9cos? (tan (3x))sin (tan (x))…

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Q: dx 2 sin x - cOS X |tan+ 2 + V5| In 5 tan; + 2– V5 |tan+2-V5 + C + 2+ V5 2. + C In Option 1 O Option…

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Q: 1+ cosx + sinx sinx 1+cos x 2sec x 2csc x 2csc 2x 2sec 2x X.

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Q: etan 4s | (cos (cos 4s)2 ds

A:

Q: Solve over the interval [0,2pi)

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Q: 15. f(x)= sin 3x 17. f(x)= tan 2.x 19. f(x)= 3 cos (x – 7/2) -

A: 15) For sin(3x) the range of the function will  be the same as sin(x) just the period, in this case,…

Q: Find x where 0 ≤ x ≤ 2π. cos²x - cos x - 2 = 0

A:

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…

A: