f6)= Sin () (x 3x26x-8) 1 CosX In Ceos x) | $66)=Sinx+t Cosx. sinsetl -6()=DSin -2053 2.

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval (o, ~).

A: Given:sinx=0.3

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

A:

Q: Q1/ Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13

A: Note: We are entitled to solve only one question at a time. To Show:…

Q: 4. Verify. COSX 1+sinx = 2secx %D а. 1+sinx COSX b. cosx(1+ tanx)² = secx + 2sinx %3D

A:

Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

A:

Q: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 5)Prove that (1+sinx)(1+sin(-x)) = cos²x (manipulate left side in order to get right side) %3D

A: We have to prove the given identity: 1+sin x1+sin -x=cos2 x We know that sin -x=-sin…

Q: tan(2x) O 1+ cos(4x) sin(4x) O cos(4x) – 1 sin(4x) O 1- cos(2x) sin(2a) sin(4x) 1+ cos(4x)

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: Prove sin 2x cot x (1 - cos 2x)

A:

Q: 2

A: Prove: cos²(x/2)=(sin²x)/(2-2cosx)

Q: Verify the identity cosh2 x = (1 + cosh 2x)/2

A: We simplify each side using the formula of cosh(x)   Left side:

Q: Find all solutions of 4sin^2xtanx−tanx= 0 that are in the interval [0,2π)

A: Given the equation  4sin2xtanx-tanx=0. We need to find the solution in the interval [0,2π)

Q: Express 2 sinx- v2 cos x in the form of Rsin(x – a), w

A: Given expression is   2 sinx -2 cosx

Q: Use th Start! 1- cos 2x

A: Given:1-cos2x/cos2x To simplify we use some trigonometric properties

Q: FIND THE REAL ROOT OF X.EXP(X) = COSX BY SECANT ITERATIVE METHOD CORRECT UPTO 4 DECIMAL PLACES.

A:

Q: tanx 4) S Edx Cosxv1+secr 5) S(1- u)vudu

A:

Q: cos 2x +1 sm 2x Prove that Please show proper steps sin 2x 1- cos 2x

A: We know the formula (1) 1+cos(2x)=2cos2x (2) 1-cos(2x)=2sin2x (3) sin(2x)=2sinxcosx

Q: solve for allvalues of x in the interval 0 ≤x≤2π:  2-2sin^2 x+3 cosx=-1

A:

Q: [2 2 sinx cosx + 3cosx7 2 cosh 3 X 1 D²+ 4 D3 D³ -27

A:

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval(o, π/2).

A:

Q: verify that (sin(x)-cos(x))^2=1-sin(2x)

A:

Q: sinx(tan(x/2))-sinx=0

A: sin x tanx2-sin x=0

Q: 51 |x* sin 3xdx 2 53 [x' sin 3xdx 55 sin 3xsin 2.xdx

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

A:

Q: prove that = - Cotx + C 1- cosx +Sin'x

A: According to the question, we need to evaluate the integration: F(x) = 2(1 - cos2x + sin2x) We need…

Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Prove that sin3x/sinx - cos3x/cosx = 2

A:

Q: x sin 2x sin COSX 8. Prove that: %3D 2x-7

A:

Q: Prove 2tan x cos (3x) = sec x (sin(4x) - sin (2x))

A: Topic- trigonometry

Q: prove that: sin7x.cos3x-cos7x.sin3x/tan2x=cos4x+1

A:

Q: prove that catX+c - Cos'x+Sin2X

A:

Q: prove that sin⁴x - sin²3x+sinx-3 = 0 has no solution.

A: prove that sin⁴x - sin²3x+sinx-3 = 0 has no solution.

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: prove that 2. = - Cotx + C |- Cosx +Sinx

A: This question is fairly based on simple formulas of trigonometry and calculus

Q: Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13 %3D

A:

Q: Find , if da y = 3x cos4x 12x* sin4x – 10x cos4x None -2x4sin4x – 12x° cos4x -12x4 sin4x + 12x°…

A:

Q: Prove (secx+tanx)/(secx-tanx) = (1+2sinx+sin^2x)/cos^2x

A: To prove that   (secx+tanx)/(secx-tanx) =(1+2sinx+sin2x)/cos2x

Q: prove that cos^2 x/2= tanx+sinx/ 2tan x

A:

Q: What is the integrable form of sin-cos-sino do?

A:

Q: Show that sin²(x) cos(x) = sec(x) – cos(x)

A: We need to show the following. So,         Manipulating right side=secx-cosx=1-cos2xcosx=sin2xcosx

Q: What is the integrable form of sin-cos-sin0 do 2 2

A:

Q: compute:   ∫sin^3xcos^2xdx

A: We have to find:

Q: find integral tan 6 x sec  4 x dx

A:

Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

A:

Q: 3-sinx 6. f(x) = 1+ In(x3 — х)

A: Quotient rule of differentiation: Chain rule:   also

Q: Verify that 2tan (x/2)= (sin2x+1-cos2)/(sin x(1+cos x)

A: Consider the given condition that,2tan (x/2) = (sin2x+1–cos2x)/(sin x(1+cos x)) … (1)Consider the…

Q: 6. tan (9x + 5) + C 1. O B. - O A. sec2(9x + 5) Which function should be differentiated? 6. tan (9x…

A:

Q: =sec (Xty)

A: dydx=secx+y  Let v=x+y  1+dydx=dvdx  dydx=dvdx-1  dvdx-1=secv dvdx=secv+1 dvsecv+1=dx

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: