9.2. If z1, z2 # (1/2) + kT, show that tan 21 = tan z2 if and only if 21 = 22 + kT, where k is an integer.

Q: 12 and x terminates in 13 nd sin 2x, cos 2x, and tan 2x if sin x= sin 2x cos 2x %3D tan 2x %3D II

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Q: If y= In(4 tan (4x) ), then y' tan(4x) = Select one: 04/(1+x² ) O None O 4/(1 + 16 x² ) 01/(1+ x² )…

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Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

Q: /2 1lf If In = " x cos" x dx, when n> 1, show that п(п — 1)1-2 — 1 In 12 [Hint: cos" x = cos²…

A: Given: In=∫0π2x cosnx dx

Q: Q3) Ify = in[sec 8 + tan 8) find

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Q: x2 – 1 if æ <1 1 f(x) = T In a a cos 2rx + b sin( 4 In 2 if 1<a < 4 2" – x2 if 4 < x - where a and b…

A: For f(x) to be continuous at x = a : LHL= RHL = Value of the function at x = a

Q: Let us determine the mth coefficient in the representation given by equation (3.212) for the…

A: cm=2N+1.∑k=1Nδk,rsinmπkN+1orcm=2N+1.∑r=1Nδk,rsinmπrN+1it mean cm has a function for k,r and both are…

Q: Suppose n is an integer. So Show that for n+0, ſ x cos(nx)dx = { п n is even (a) 2 п is odd n2

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Q: [5] Determine the y(2021) of y=cos²

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Q: 4) state laylors your estima te 5) Using in Taylor's Theorem, show that the error in 3) for cos…

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Q: 6. Let z1 = x1 and z2 = x2, with x1, X2 real, and the relationship ei(x1+*2) = etx1ętx2 to deduce…

A: A detailed solution is given below

Q: Find the exact value of the following 1.) sin30° + csc60° 2.) 5sec 30 an60° 3.) 3sin45° + 4cos45°…

A: Given :   Trigonometry value

Q: 3.) If g(x) = cos 2x ,Find g ().g ), g(-x), g(n – x), g (n + x),g(x -)

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Q: 7) Suppose a is a positive constant less than 7. Prove that the equation 2r+cos r = a has a real…

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Q: cos(3rk) In k 5k k 1

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Q: 21. Let h(x) = tan(5x + 6). Then %3D h'(2) is and h"(2) is

A: 21) The given function is: h(x)=tan(5x+6) To find h'(2) and h''(2)

Q: 5. Estimate to 4th place accuracy, i.e. within 0.00005 of cos(2º) using its Mac- xpansion. Justify…

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Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: 7) Suppose cos(x – y) = xy. Find at the following points 7.1) (0, 5) 7.2) (0,– 5)

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Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: 1) VERIFY THE POWER REDUCING FORMULA, cos"x : cos 2x+1 HOLDS TRUE FOR 2 x = - AND x =

A: To verify:   cos2x=cos2x+12, for x=π3 and x=π2   NOTE: As per our answering guidelines, we can only…

Q: if x <1 x – 1 | f(æ) = T In x -) if1<x < 4 4 In 2 %3D a cos 27rx + b sin( 2" if 4 < x | where a and…

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Q: 4) Find the value of cos(1.74) from the following table oot x y = sin(x) Hint: dy dx 1.7 0.9916…

A: The given problem is to find the value of cos(1.74) by using newton divided difference method from…

Q: - IF z = tan2 -1 y Show that x- ây

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Q: 13. Sdx = A tan-1를+k tan-+* C In(x + 4) 1) In(x + 4) + k 13. x +4 13

A: To find integration of the given function f(x) = 1/(x +4)

Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 0, + tan 02 + tan 03 + ......... + tan…

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Q: Chapter 12, Section 12.1, Question 003 Find the domain of r(t) and the value of r(to). r(t) = cos…

A: r(t) = cos(πt)i-ln(t)j+√(t-8)k

Q: 15 Find sin 2x, cos 2x, and tan 2x if sinx and x terminates in guadrant III. 17

A: Given that: sinx=−1517 To find: sin2x, cos2x, tan2x

Q: Find θ with 0≤θ<2π  and tanθ=1

A: 0≤θ&lt;2π  and tanθ=1

Q: The solution of tan x = -V3 in [0, 7) is x = 7 If n is any integer, all solutions of 3 or x = tan x…

A:

Q: Show that in (5.2) the average values of sin mr sin nx and of cos mI cOs na, m+ n, are zero (over a…

A: Given problem is :

Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: 2. If 90° < 0 < 180° and cos 0 =-, find sin. %3D 11/3 11/3 3 ) - 3V11 11 O 3/11 11

A: We know that the trigonometric identities :  cos x = 1 - 2 sin2 (x/2)

Q: 8 and x terminates in guadrant IV. 15 Find sin 2x, cos 2x, and tan 2x if tanx %3D

A: Given  tanx=-815,  x in quadrant IV

Q: 42. What is tan 0-1 Ove IN/MS/N/N 2 0_V2 2 O √3 377 4 2 ?

A: tan (π - x) = - tan x

Q: 0. If 180° < 0 < 270° and cos e = -, find sin 20. %3D 13 O- 16V105 169 O 16/105 169 O sV105 169 O -…

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Q: 4 Find sin 2x, cos 2x, and tan 2x if cosx= and x terminates in guadrant III.

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Q: 4 Giren tan A =– where 0<AS Find 2sin 2A.

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Q: If y= In( 8 tan-1(8x) ) , then y' tan-1(8x) = Select one: O 8/(1+ 64 x² ) O 1/(1+ x² ) O None O…

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Q: Find the exact values of sin 20 and cos 20 for cos 0= 3 on the interval 0° s es 90°. 18 35 cos 28-…

A: cosθ=318    ,  0°≤θ≤90° By using the identity sin2θ+cos2θ=1, we get…

Q: For cos2(xy) = - evalu COS 4

A: Given

Q: Prove that for all k E N, [cos0 -sin0 [coske -sink0 sine Lsink0 cose cosko

A: To prove this result we use the matrix multiplication.

Q: 7.32. Prove that for 05sr, -( . ) cos 2 cos (a) a(e -a) = sin 3r sin ba (6) (r-) - 7.33. Use Problem…

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

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Q: Find sin 2x, cos 2x, and tan 2x if tanx=-. and x terminates in guadrant IV 3

A: sin 2x= 2 sin x cos x cos 2x=1-2sin2x tan 2x=(sin 2x)/(cos 2x)

Q: Find the exact values of sın 20 and cos 20 for cos e on the interval 0° S 8590° sin 20= 0.7744, cos…

A: Use the identity sin2θ+cos2θ=1 to evaluate the value of sin θ. sinθ=1-cos2θ=1-372=1-949=4049=2107

Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…

Q: (d) Show that there is some x with 0 < x < 2 such that x2 + cos(ax) = 4. %3D

A: Solution-