3x2 sin(x³) Select one: а. In/tan x3 + cot x³| + c b. -In csc x3 + cot x³| +c С. с. In|sec x3 +tan x³| + c d. In sin x3 + cos x³| +c

Q: COS X sin' n - Show that for n > 2, | sin x dx sin"-2x d.x n Use this to find sin x dx.

A: ∫f(x).g(x) dx = g(x).∫f(x)dx  -  ∫g'(x)∫f(x) dx   where f(x) is second function and g(x) is a first…

Q: f tan x = -5, and cos x > 0, find sec x and cos x 26 26 and cosx = 26 sec x = sec a = 26 and cos x =…

A: Solution-

Q: 10- Sin'x- cos'x is equal to: a)2x b)1 c)-1

A: 10-sin^2(x) -cos^2(x) We apply trigonometry rule

Q: (c) Prove that sin x 7C sin 2 x2 dx +4x+5

A: The integral function is ∫-∞∞sinxx2+4x+5dx

Q: tan(tan3x)dx Evaluate: cos-3x -In |sec (tan3x)| + C (B ® - in [cos(tan3x)| + C © - sin( tan3x)| + c…

A: We need to evaluate the following integral I = ∫tantan3xcos23xdx…

Q: To begin evaluating S sin*(x) · cos³(x)dx, express a. sin*x to (sin²x)²and use the identity sin²x…

A:

Q: Estimate the error if P 3(x) = x - (x^3/6) is used to estimate the value of sin x at x = 0.1.

A: Given:

Q: 1. Explain why sin(n+0) =-sin@ using a diagram and x, y, and r.

A: Solution of given problem is followed by

Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: a) Show that sin¯'x + cosx = 2 E) - tan-' (). x(x-y) y(x+y) (b) Find the value of tan1 where >-1…

A: We can solve these two question by using the properties of inverse trigonometric function as below.

Q: 3. Prove that the identity is true. sin*t- cost = tan²t-1 cos't

A:

Q: EX-15- Prove that : a) Sec-'x= Cos- ! b) Sin-' (-x)=-Sin-'x

A:

Q: Verify the identity: (sin x - sin y)/(cos x - cos y) = -cot (x+y)/2

A: sinx-sinycosx-cosy=2cosx+y2sinx-y2-2sinx+y2sinx-y2=-cosx+y2sinx+y2=-cotx+y2…

Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: cos 2x +1 Prove that sin 2x

A:

Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

Q: -- cos( sin-!x) + C 1-x² A True B) False

A: SOLUTION-

Q: Let y=f(x)=sin^2(x)-cos(x)+2sin(x)+x find f'(x), factor f'(x) and determine the critcal values on…

A:

Q: 2. Apply the properties of even and odd functions to find the exact va a. sin(-120°) (-#) c. sin…

A:

Q: coS X sccr+ tan x 1- sinx

A: given,        cosx1-sinx=secx+tanx

Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: (2k + 1). True or False tan 0. cos 0 = sin 0 for any 0 + %3D

A: Given :            tan θ . cos θ = sin θ for any θ ≠ (2k + 1)π2.  To state true or fase.

Q: Estimate the error if P3(x) = x - (x3>6) is used to estimate the value of sin x at x = 0.1.

A:

Q: Q4: Prove that: cos?x – sin?x cos²x - 1- tan?x

A: We need to prove that cos2x-sin2xcos2x=1-tan2x We will use tanx =sin xcos x

Q: Complete the statements.

A: Given Our aim is to complete the sentence

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: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

Q: 8. Evaluate sin (x) cos(r)dr using an appropriate substitution.

A: here  we use the formula  ∫(xn)dx=xn+1n+1+C     according to our guidelines we can answer only…

Q: Prove the identity: sin (x-y) tanx- tany cosx cosy

A:

Q: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?

A: Now we use identity  Sin2x +cos2x =1 And formula (a+b)2= a2 +b2 + 2ab  (a-b)2 = a2 + b2 - 2ab

Q: Find x where 0 ≤ x ≤ 2π. 4 cot²x = cos²x + sin²x - 1

A:

Q: 5) f(x) = tan [In{sin(15x - 30)}] %3D

A: For this problem we have to apply derivation to each term.

Q: Find all solutions of v3 tan xcotx + V3 tan x - cot x-1= 0

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: šx<2a . dation where 1 1. sin x = 2 2. 3tanx-1=0 3. 2cosx=cosx

A: We will find the values.

Q: Q4) Prove that 1- Cos +x) = sin x, 2- (sin x +cos x) sec x see' x

A:

Q: Choose the correct answer If f(x)=ln⁡(cos⁡(3x)) , then f"(x) =…  -9 sec2 (3x)  9 cos2 (3x)  9 tan2…

A: Derivative problem....

Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: Complete the statements.

A: a). As x→-1+, sin-1x→-π2

Q: Derive a formula for ſ tan x sec "x dx where n 40

A: Integration problem....

Q: lim,-o-cos(2.x) →0°sin²(3x) Q6- Evaluate:

A:

Q: 1. Given tanx = - and cos x >0, find secx. A. в. C. V10 D. 2V10 2. Given secx and sin x 0. 3. Find…

A:

Q: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

Q: If f (x) = - sin(x), then f (10) (x) is equal to = - sin(x), thenf (10) (x) is equal to A - sin(x) B…

A:

Q: What is the exact value of sin ( cos (-)) + tan- (sin (5))? 2/2-a 4 -2v2+x 2/2+ -2V2-n 4.

A:

Q: 3. Given f(x) = cot(x) sin(x) and g(x) = cos³(-x)(sec² (x)-1) sin² (x) a. Prove that f(x) = g(x).…

A: Given that,  fx=cotxsinx and gx=cos3-xsec2x-1sin2x

Q: Prove the identity : sin(x-y) tanx- tany Cosxcosy

A: Consider, tanx-tany=sinxcosx-sinycosy=sinx cosy-cosx sinycosx cosy=sinx-ycosx cosy…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.