tan²(0) – 5 tan(0) + 6 = 0

Q: f(x) = (2x3 tan(x) – e-*)10 and g(x) = /(3x – 4)² – sin(x). %3D %3D

A: We have to use the chain rule to find the derivatives of f(x) and g(x)   We also have to find…

Q: cos (x sin )=√₁ (x)+2 J₂ (x) cos 26+2 J₁ (x) cos 44+... sin (x sin )=2 J₁ (x) sin +2 J, (x) sin 36 3…

A: Using generating function of Bessel functions

Q: 2x - 6x 34. lim x-0 sin 2x 35. lim 2 1- cos 2

A:

Q: tan3x)dx tan Evaluate: cos23x A - In|sec (tan3x)|+C - In|cos (tan3x)| +C B © In cos(tan3x)| +C in…

A:

Q: 2 sin²(x) – 3sin (x) + 1 = 0

A:

Q: 2+tan x cos³ x

A:

Q: tan (3r) dr = a tan(3x) – In(v1 + 9x²) +C 3 a tan (3x) + In(v1+9r²) 3. e tan '(3x) In(v1 - 9x² +C a…

A: We know that, from basic integral formula ∫tan-1x=xtan-1x-12log1+x2+C          ⋯⋯1 We have, the…

Q: 15) tan-l –1 --1 V2 17) cos 2 1 19) tan- 1

A: Given: 16)  tan-1-1

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

A:

Q: sec42x -dx tan 2x 1 1 12 tan 62x Find 1 1 A 16 tan 82x ⓇB (cor -=— 1+3csc²2x 12 cot82x) (4sec 22x-1)…

A: Evaluation of the indefinite integral by using substitution method

Q: cos 2x-1 i) x sin 2x 2 tan 30–20 ii) tan 40

A: follow next step.

Q: 3. tan(xy) + xy -0

A: Question number 3,Given,           tanxy+xy=0To find : The second derivative, y'' of the given…

Q: 1-х 2. cos-1x = tan-1 V1+x

A:

Q: Write the expression as an algebraic expressionin x for x>0.   b.  tan (2 cos-1(3/x))

A: Given expression can be represents as: tan2cos-13x  for x>0. Let us suppose θ=cos-13x  then the…

Q: 4sin(x)cos (x)+2sin(x)-2cos(x)-1=0

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 2 cos I Use a counter-example to show that cos 2x

A:

Q: Integral: Evaluate -2 sin 2x xp= V9+ cos² 2x

A:

Q: sin²k Σ 2* k = 1

A: For the solution follow the next step.

Q: Find (f-1)'(a). f(x) = 2x3 + 5 sin x + 3 cos x, a = 3 %3D (F-1)'(a) = %3D

A:

Q: y = x cos(In x)+x² In x²

A: d dx(cosx) = -sinxddx(lnx) = 1xddxx2 = 2x   Product rule u.v = u'.v + v'.u

Q: -1 1- x² 1+x? Differentiate cos with respect to tan -1 2x 1- x2 '

A: Derivative of one function with respect to another function. Using substitutions to find derivative.

Q: -1 x-1 +tan x+ n(-7) tan T+tan x-1

A: Introduction :

Q: cos(x1)=-1/3 sin(x2)=2/3 find 1. sin(x1+x2) 2. cos(x1+x2) 3.sin(x1-x2) 4.cos(x1-x2)

A:

Q: a. [CO²2 2 cos²x√4 tan x tan² x da

A:

Q: d x 2. 1+xVI-(Tanin)

A:

Q: tan6(x) cos4(x) sin²(x)sec³(x) [7sin²(x) + 9cos²(x)] + C A 63 tan²(x) [7tan²(x) +9] + C B 36 Ⓒ…

A:

Q: TOLLOWLNY tan x+ 4 tan 2x - 3 tan 3X Lim x°tanx i)lim| cos-cos COS ....coS

A:

Q: (x²-2x) (In x³-3 tan x) x√x

A:

Q: Antiderivative of sec(3x)tan(3x)

A:

Q: C. tan 0 = 3 sin 0 over [0, 2n) %3D

A:

Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

A:

Q: x = -30°, cos 2x = 1 - 2 sin2 x 1 + 2 sin 2 x 1 - 2 sin 2 x 1 - 2 sin x 1 + 2 sin x

A: This question is based on Proving a Trigonometric equation.

Q: sin- x - y· dx + (tan-(yx-1))xdy = 0 cos-12

A: The given differential equation is x-ysin-1yxcos -1yxdx+(tan-1(yx-1))xdy=0. Simplify to obtain the…

Q: tan(x) dx cos4(x) tan'(x) A [7tan²(x) +9] + C 36 1 ℗tan'(x) + tan³(x) + C C D sin²(x)sec³(x)…

A:

Q: ( tan( tan3x)dx Evaluate: cos²3x A -In |sec(tan3x)| + C 3 |cos(tan3x)|+C B © --n |sin(tan3x)|+c O…

A: Evaluate: I=∫tantan 3xcos2 3xdx

Q: BIARI dr x Cos (1-1)dt b) sin² x c) cos³ x d) - cos²x

A:

Q: 3x2 lim x→0 cos(2x) – 1

A:

Q: tan" -1 I# Z-X FEMD fyx At (-,1).

A: The solution for the above question is as shown below.

Q: 2 tana-2 tan b = 2 tan x -1 tan a- tan b = tan¬1 x %3D a-b - a-bten- 1+ab tan = tan a-b X =- 1+ ab…

A:

Q: R-4 (1-tan x) (1+tan x) dx evaluates to

A: Introduction :Here we have asked to solve the given integration.

Q: V2 V2 - 1 cos -1 (a) sin (b) (c) tan-'(-1) - 2 2.

A: Given equations are a)sin-1(-22)b)cos-1(-22)c)tan-1(-1)

Q: = sin? (esin" t) + cos-1(2t3 (x) = tanh-1 x + In V1– x2 |

A:

Q: X+1 1-x Select one: a. sin-1(x)-V1-x² +c www. O b. sec-(x)-V1-x? + c C. tan (x)-V1-x2 + C d. cos x)…

A:

Q: 2) + (2x tan-" y – x³)(1+ y²) = 0 Ans: tan-y=(x² + 1) + ce-*²

A: Bernoulli differential equation in the form of: dydx+k(x) y=q(x) yn 1yndydx+k(x)×1yn-1=q(x)…

Q: sec4 x 21) tan3/2 x A) _ -1 + C tan1/2 x B) - 14 tan- 1/2 x sec4 x + 7 tan-3/2 x sec5 x+ C C)? tan-…

A: Here is the solution

Q: • tan°(x) Xp- cos“(x) 1 1 tan9

A:

Q: tan-1 x (х-у) tan-1 x+y. > -1 y(x+y) where ().

A: Known fact: tan-1A-tan-1B=tan-1A-B1+AB.

Q: Differentiate

A: Given,

Q: sin 2x J-1 x8 +x* – x² +2

A: Evalute the integration ∫-11sin2xx8+x4-x2+2dx.