+sin(n")n-1 n6.1+cos(n2)n®+2 4. 2 9) Et sin (n* cos(n)

Q: (1+iV3)"+(1-i/3)" %3D 2n+1 Sin(- 3 2" Cos( ) 3. 2n+ Cos( 3. 2" Sin 3. (1-V3

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Number 33

A: Given,

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

A:

Q: 6(cos² x – 1) x – 1) sin x cos a – sin z O 6 tanx + 6 sec z O 6 cot x+ 6 sec x O 6 tanx + 6 csc z O…

A:

Q: If e /2i =sin2 then z = 2i In(sin2) + 4k TI - 2i In(sin2) – 4k TI - - 2i In(sin2) + 4k TI - -2…

A: Use the principal log to find z.

Q: 1/1+cos x + 1/1-cos x=2csc^2 x

A: Please refer the attached image for complete solution.

Q: sin 2x + 2 5я 3 + n, 3 5я + 2 n, + 2 яп 3 3 5я + KN, 6 2 я ○쓸+2.0, + 2 n 6 3

A:

Q: 2) sin- 0 4) cos 6) cos-1 | V3 8) tan 3 -1 -1 10) cos

A:

Q: Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7]

A: Given y = 4 cos(x) - x

Q: Verify the identity. cos(+ x) + cos(-x) = = COS X X- cos(+ x) + cos(-x) = 2 cos ( 2 COS ( + + x + =…

A:

Q: 1 cos²0 1 sin 9 1 tan 8 + tan 8 + || || Trigono 1 sin² 0 cos²0 1 sin cos 0

A:

Q: 1/sin(x)/cos (x)+cos (x)/1+sin(x)=4 Prove

A: For x= pi/3

Q: sin- In?| 4+ tan-!cos- dx 1+ cos2- 4+ tan-cos- 2sin- In2 4+ tan-'cos- dx 2 2 A 1+ cos 4+ tan-'cos- х…

A: Given integral ∫sin x2.ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

Q: lim sin(k/n). 1. cos(1) +5/3. 2. cos(1) +1/3. 3. cos(1) +2/3 4. cos(1) – 1/3.

A:

Q: sin 5x + sin 3x 2 cOS X 4 sin x cos 4 sin x cos x 3 X COS -

A:

Q: Estimate the root of the expression, f(x) = x² – cos x, using: b. False Position Method in the…

A: The False position method is a technique used to find the approximation of the root of the equation…

Q: Prove the identity. 1+ tanh(x) = e2x 1- tanh(x) 1 + cosh(x) 1+ tanh(x) 1- tanh(x) 1 cosh(x) cosh(x)…

A:

Q: sin (3x) + cos (3x) cos(x) – =1+4sin(x)cos(x)

A: We use sin(3x)= 3sinx-4sin3x and cos (3x)= 4cos3x-3cosx .

Q: 1 1 Express in terms of csc(x) 1+ cos x 1- cos x

A: Given:     To determine: The given expression in terms of cscx

Q: 3tan3x=tanx in the interval [0,2pi

A: Given,3 tan3x = tan x3 tan3x - tan x = 0tan x (3 tan2x -1)=0tan x =0            ;     3 tan2x-1 =0…

Q: *k) 1- (sinº x+cos x) = 3 sin² x cos²x

A:

Q: 2sin(x)cos(x) = sin2x Is it a legitimate operation to divide all x's by 2 to get:…

A: Solution, The general formula for this trigonometric expression is -  Sin(2x)= 2sin(x)cos(x)   Here…

Q: Proof 2: 14 sin x dx tan xdx = /6 COs x 1 -= sec x dv = sin xdx cos x du = sec x tan xdx v =-cos x…

A:

Q: sin(k/n). 1. cos(1) + 5/3. 2. cos(1) + 1/3. 3. cos(1) + 2/3 4. cos(1) – 1/3. O 1 O 2 O 4

A:

Q: n+2 n+3 * ₁ (₁ - ¹) - ₂ (~ + ²) + + ₂ (²+ ³) + (n+¹) sin + sin sin n n lim n-x N + ... + sin (2) =…

A:

Q: 7. хЗуб + е1-х — cos(5y) %3D у?

A:

Q: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

A:

Q: V1+ cos x + v1- cos x X =-+-,0<x<. 4 2 an 1+ cos x - V1- cos x - cOS X VI

A:

Q: 6(cos² x – 1) sin a cos z – sin z O 6 cot x + 6 sec x O 6 tanz + 6 csc x O 6 sin z + 6 cos a O 6 tan…

A:

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: 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: 4sin'x – 1 1. 2sinx + 1 = 2sinx – 1 sin'x – 2sinx + 1 2. = sinx – 1 sinx – 1 3. ( sinx - cos x)(sinx…

A: Simply use the basic concepts of algebra and simplify the each one.

Q: 1+cos 4x Express without double angles. sin 4x O (cot a + tan x) O ÷(cos x 글 (cos sin x) - O (cot a…

A:

Q: 6 x° cos(x) dx =. 6 x³ sin(x) + 18 x² cos(x) – 36 x sin(x) + 36 6 x³ sin(x) – 18 x² cos(x) – 36 x…

A: Integration by parts  ∫udv=uv-∫v.du

Q: prove that cosh^2x-sinh^2x=1

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

Q: cosxtanx - cos x= 0 + O 0+n,+ 2nx 5я O O+*5, + 2nx 5я

A:

Q: cos(x (*). cos(x + h) – cos x cos h – 1 sin h - - sin x · h COS x h h

A: Require to verify the identity cosx+h-cosxh=cosxcosh-1h-sinxsinhh

Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

A:

Q: sin^2 x + sin x cos x over cos x − 2 cos^3 x

A: This question is based on Trigonometric Formulas to simplify question.

Q: (5) f(x) = cos (5 - 2x) (7) f(x): = cos (√x³ + 1) (9) f(x) = cot (x5) (6) f(x) = cos (4x7 + 3) (8)…

A: Note: As per company guidelines we solve only first three subparts when multiple parts question…

Q: sin + 4 4 can be expanded to: sin sin 4 4 cos cos 4 o sin - cos 4 sin 4 sin 4 o cos -sin 4 + cos 4…

A: Solve the following

Q: Integral of sin^4 (x/2) cos^2 (x/2 dx

A:

Q: 2) tan-l 1 Vz 4) sin-! 6) tan-1V3 8) tan-l 0 V3 10) sin-! V3 12) tan- 2. 2. 3.

A:

Q: sin(cos (0.715)) O 2.6991 O -1.3009 O -0.3009 O 1.6991 O 0.6991

A: Given,               sin(cos-1(0.715))

Q: 5.) cos (x -) + sin ( – x) = cos x cos (x -) + sin ( - x) = 3

A: Since multiple questions are asked, according to guidelines answering first question. Cos60 =1/2…

Q: Find x where 0 ≤ x ≤ 2π. cos²x - cos x - 2 = 0

A:

Q: () - VE ()- 1+cos 0 1-cos 0 Show that cos and sin (: using de Moivre's Theorem.

A: