(i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in radians for whicl- 3 3 -2 sinxcosx= sec 3x(sin3x--2 sin' 3x). 3

Q: Find the periodic function f(x) = sinx + tan-+ sin- X + 23 + sin 2n+1 + tan ... 2n

A:

Q: 3 Find sin 2x, cos 2x, and tan 2x If cosx= and x terminates in quadrant II. sin 2x cos 2x tan 2x

A:

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

A:

Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: 15 and x terminate: 8. Find sin 2x, cos 2x, and tan 2x if tanx = sin 2x |3| cos 2x

A:

Q: 1. ) cos (4) COS -π/2 f/² sin (1) sin (²) dx (Consider initially the first 2 terms)

A:

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: 15. cos³ 3x 3√√/sin 3x dx

A:

Q: f/² sin (1) 4x ; (**) sin (²) COS (²) dx (Consider initially the first 2 terms)

A: ∫vn dv =vn+1n+1+C

Q: 3 (4+sin-15x)° dx (8) V1-25x2

A:

Q: (3.2 cos 2x+2 -dx. 1.8 1+ In x Use NINT on the calculator to evaluate:

A: We have to evaluate ∫1.83.2 cos 2x + 21 + ln x dx.

Q: 10x 19) y Sin'(5x') (ans.: JI-25 x' 20) y= Cot ) (ans.: 1+ x' 6x' 21) y=tan'V4x'- 2 (ans.: (4x'-1…

A: As per guidelines we can only solve first question or first three subparts of the question, I am…

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: 4 Find sin 2x, cos 2x, and tan 2x if tanx and x terminates in quadrant IV. 3 sin 2.x cos 2.x tan 2.x…

A: Given:- tan(x) =-4/3 To find:- value of sin(2x), cos(2x), tan(2x)

Q: 3 Find sin 2x, cos 2x, and tan 2.x if cos.x = and x terminates in quadrant II. V10 sin 2x %3D

A: given

Q: Find cos(4x) sin(4x) da.. To cos(4x) sin(4x) dx : =

A:

Q: tion for sin x= 0.3

A:

Q: (2 cos 2x+ 3 sin 2.x) 7. evaluated at x = 1 rad

A: Given query is to find the value of the expression at x = 1.

Q: 7/4 (sec² x – sin x)dx

A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

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: sin(-4x) cos 3x dx 1. 3

A:

Q: Suppose: sin(x) = -0.1 cos(y) = 0.5 tan(z) = -4.3 Then, sin(-r) =| 0.1 cos(-y) = 0.5 tan(-2) = 4.3…

A:

Q: 4 cos () dx 10. x³ sin3

A:

Q: cos 2x+1 sin 2.x 7. Prove that sin 2x 1-cos 2x

A: The trigonometric of an acute angle in a right triangle express the relationship between the angle…

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

A:

Q: of sin (4) sin³2 x sin 2x dx

A:

Q: 12 tan (4.x) sec (4x) dx S cos(11x) sin(2r) dx COS

A: Given that integration and we solve this integration by using general formulas of integration. Here…

Q: 15 Find sin 2x, cos 2x, and tan 2x if cos.xr= and x terminates in quadrant IV. 17 sin 2x cos 2x !!…

A:

Q: 1 what are possible values of cos x and tanx? 2 If sinx= Select one: V3 and tanx= 2 1 a. cosx= V3 V3…

A: Consider the right triangle with one angle x degree. Let a be the length of the adjacent side and b…

Q: Differentiate  x sin−1(x)  with respect to sin−1x.

A: Using derivative of one function w r to another function.

Q: (7) Find sin(5x) cos(4x) dx

A: Topic:- application of integration     Note:- as per our guideline if more than one question…

Q: 1. Show that | sin x cos3 x dx = sin® x sin x +C = - 8. cos*x, cosx cosx +C 3

A: To prove:-

Q: cos^2x+sin^2x/cos^2x=

A:

Q: 1- cos 4x sec2 2x – 1 = 1+ cos 4x

A: Question is solved.

Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

A:

Q: ating / * sin (2x)cos(2x) dr by substitution, if u= sin(2x) th

A:

Q: 1- cos 4x 9. sec2 2x – 1 = 1+ cos 4x

A:

Q: 11 tanto-2 tan Bz1 show that 2 coste- Cos B20

A:

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: 37. cos 6x dx 40. sin x? dx 39. cos do 42. tan x sec² x dx 41. sin 2x cos 2x dx csc2 x dx cot x sin…

A:

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

A:

Q: 2. / sin² cos² xdx

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: B. - sin3 p cos 3p sin 3p cos 6p – sin 6p cos 6p H. sin 6p - cos 9p - sin 9p K cos 9p sin 9p LL

A:

Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: 8 sin(2x) cos(2x) dx

A: We have to evaluate the given integral

Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

A:

Q: sin(4 + 5x) cos (5x – 4)dx

A:

Q: dz 5 – 2x cos 2x dx 1 + sin 2x sec² 0 de. tan 0

A:

Q: Verify the identity. sin 3x 1 = 2 cos x- %3D sec x 2 - sin 2x

A: Given: Verify the identity sin3xsin2x=2cosx-12secx for verifying given identity we solve left hand…