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 sin x) O (x + cos x) sec² (x sin x)

Q: 4. y = 5 cos 4x, 3rd derivative 5. y = 3 tan 3x, 2nd derivative %3D 5. y = 6 csc x, 2nd derivative

A:

Q: secx-tan x cos x %3D 1+sin x secx+tanx

A: consider the left hand side of the equation sec x -tan xsec x +tan x sec x -tan xsec x +tan x=1cos x…

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: 7. h(x) = tanx- tan 8. h(x) = 3 sec-x

A: we have been given the equations to differentiate w.r.t x

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…

A:

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

A:

Q: 3. lim X-0 sinx sinx-cosx 4. lim x- 5. lim x(cosx-1) sinx-x

A:

Q: limx→0  (x^2+3) / (1−cosx)

A: given example is, limx→0x2+31-cosx

Q: 2 tanx + 7tanx+ 5 sec2x 2 tanx + 5 X. %3D

A:

Q: (tan x) = fu. v dx = (sin x) = | -=-=dx = (cos x) = fe" dx = | (arcsinx) = sec x tan x dx = secx tan…

A: We have to find out derivative and integral

Q: ftan (x}sec"(x)dx Scot (x)csc°(x)dx Ssin (x)cos°(x)dx

A:

Q: sin x cos 4x 32) lim X0 X+X cos 5x

A: Consider the given limit

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: ON 3 sec3(In x) + sec2(In x) tan(In x) 2х n x) tan(In x) n x) dx c³(In x) + sec²(In x)

A: We have to choose the correct option according to the given information

Q: limx→1 3 (x-1) tan(x³²-x) (x+1) sin²(2x − 2) -

A:

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…

A:

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: lim cos2x-1/sinx x-> 0

A:

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

A:

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

A:

Q: 8 sin x cos x sec x =

A:

Q: secx-1 sin x %3D V secx+1 1+cos x

A: It is basic trigonometry identity

Q: x2 sin x+2x cos x f'(x) = cos²x

A:

Q: [sec² x (1 + tanx) Vtan² x – 9 tan* x| dx

A: Formulae used:…

Q: Non Homogeneous LDE yIII  -  yII  =  3  + sin x

A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

Q: eCoS ecos x sin x dx In x 2. Vx 3. tan'x dx

A:

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: [(2tan(x)/1+sec(x))+(2+2sec(x)/tan(x))]=4csc(x)

A: Consider the left hand side,

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 +…

A:

Q: 7) f(x) = sin² x+ cos² x %3D Cosx-Sin X Sin X Sinx t cosx

A: Given

Q: of y= sec(x*) . 4. Find 2xsec(x?)tan(x²) sec(2x) tan(2x) O sec(x³)tan(x²) 2sec(x)

A:

Q: 1 sec x – tan x sin x = %3D secx

A: Consider, secx-tanx sinx=1cosx-sinxcosx·sinx=1cosx-sin2xcosx=1-sin2xcosx=cos2xcosx…

Q: Lim -> 0 Sin3ycot5y/ycot4y

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

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: tan x sec2 x dx tan“ x sec“x dx 83. 84. (x + 2)Vx + 1 dx (x + 1)Vx² + 2x dx 85. 86. sin x (tan x –…

A: Dear Student,  I am solving here Q. 83. In case you need help with the other questions you need to…

Q: )etan²x f'(x) = (tan² x)et %3D Option 2 g tan?x f'(x) = (2 tan x)e

A:

Q: / Vtan(x) d.x sin(2r) I Vtan(x) -dx sin(2x) -d.x sin x cos x /cos x 2 Multiply by something that is…

A: We have to find integration

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-…

A:

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

A:

Q: tanx(1+cot^(2)x)=(1)/(cosxsinx

A: To prove tanx1+cot2x=1cosxsinx consider the left hand side  tanx1+cot2x=1cosxsinx we know that…

Q: cos 2x-sin x 4. -(tan x +secx) %3D sin 2x - cos x

A: Given: prove that cos2x-sinxsin2x-cosx=-tanx+secx For verifying given expression, we solve left hand…

Q: sinx + sin 2 Evaluate | cosx A. -In cos x|– x+ C В. In'secx-x+ C C. -In|sec x|+ x+C D. In sec x|+x+C

A:

Q: secx-tanx cos x secx+tanx 1+sinx

A:

Q: lim sin2x/ x            x---&gt;0 lim tanx/tan2x       x----&gt;0

A: Multiplied the numerator and denominator by 2When x-&gt;0 then 2x-&gt;0Answer: 2

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

A:

Q: secx-11-cos.x sinx secx +1

A: We have to prove