Show that : |sin x |= CoS nX Σ n2 even 414 2/7

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. Prove the following identity: sin (x+y)sin (x-y)=cos² y-cos²x X =COS - COS¯ x X.

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Q: if x is in III, and cos x= - 8/17. Determine the exact value of sin 2x and cos 2x

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Q: 2 Given tan 0 = -and sin 0 > 0, find cos 0. %3D Cos 0 _ 3/13 13 О А. O B. cos O 0 = 3/13 COS %3D 13…

A: The given data is: tan θ= -23  and  sin θ> 0

Q: 103. Prove that for all whole numbers n > 1, sin x = sin (x + d" dx" Hint: Use the identity cos x =…

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Q: 8. Show that sin a (1+ tan a) + cos a (1 + cot a) = sec a + csc a.

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Q: Show that sin mx cos nx dx = 0 for positive integers m and n: i using the primitive, ii using…

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Q: 2. Extend the identity cos(ax)-cos?x-sin'x for xE PR to the identity cas (a2)- Cos s 2-sinz for & €…

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Q: S Show that L(cos² 3t – sin² 3t)= 82+36

A: Using Laplace transform,

Q: prove the identity  sin^4(t) - cos^4(t) = 2sin^2(t) - 1

A: We know that ,  sin 2 ( t ) + cos 2 ( t ) = 1  cos2 ( t ) = 1 - sin 2 ( t )

Q: If tan then 1– 2 1+ z2 COS X 8 |N

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Q: Assuming In = [ cos" xdx. and n > 2: 1 п -1 n-1 r sin x + -In-2; CoS' In n %3D n

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Q: Fill in each blank so that the resulting statement is true.

A: STATEMENT-1 Given equation is, sinx=22⇒sinx=12 The General Solution of the equation in the interval…

Q: 10. Prove that (지12 sin 8 cos 1 (cos a cosec 0) de 1/2-a (1-cos a )

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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: Find the values of x in 4 cos2 x = 1

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Q: Use the Intermediate Value Theorem to prove that sin x − cos x = 3x has a solution, and use Rolle’s…

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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: Show that (cos x + isin x)n= cos nx + isin nx whenever n is a positive integer. (Here i is the…

A: We can prove given result by mathematical induction: Define a statement p(n).  Show that p(n) is…

Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9x)-cos(4x) +c Select one: True O False

A: topic- indefinite integral

Q: 1 Show that sin e 8 cos (20) + 2 cos (40).

A: We need to show that, sin4θ=38-12cos2θ+18cos4θ

Q: Let sin A = - with 270° SAS360 and cos B% = 24 25 sin(A + B) 4/5

A: The given values are Now, to find the value of sin(A+B), use formula

Q: (-1)"x2" Σ (2n)! 1. For all x E R, cos x = n=0 +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b)…

A: We have to prove the sum of series.

Q: 1 Find sin 2.x, cos 2x, and tan 2x if and x terminates in guadrant IV. 10 cosx=

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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: 1) Using the formula: cos(x +y) = cos x cos y - sin x sin y, prove in steps that: cos? x = %3D 1+cos…

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Q: If S(x) = - cos(x), then s ()(x) is equal to A – sin(x) - cos(x) В sin(x) cos(x)

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9 x) - os Select one: True O False

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Q: 2. Suppose tan x = 3 -- with < x < 2n. Find the exact value of cos ). Show you work carefully. ensem…

A: Given problem:- tan(x) =-4/3 with 3π/2 &lt;x&lt; π To find:- Exact value of cosx2)

Q: Use the fact that (-1)"x²n cos(x) = L(2n)! n=0 for all x eR to evaluate cos(x²) dæ, correct to…

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Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: 4. Verify the following identities: a. sin 3x = 3 sin x-4 sin3 x b. 1+ cos 10x = 2 cos? 5x %3D

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Q: 7 a Show that for all positive integers n: 27 2n sin nx dx = 0 ii cos nx dx = 0

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Q: 3. Show f cos2n Ode 277 sin-n Ꮎ ᏧᎾ = 27 22n 11.1 n = 1, 2, 3,...

A: Using Cauchy integral formula.

Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

Q: Prove that 55 sin x² dx - 5 cos x² dx = 1/2 √

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Q: How do you evaluate ∫ sinmx cosnx dx if m is odd? What if nis odd? What if m and n are both even?

A: If n is odd use substitution with u=sin x, du=cos xdx and convert the remaining factors of…

Q: Verify the following identities: a. sin 3x = 3 sin x-4 sin x b. 1+ cos 10x = 2 cos 5x %3D

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Q: /2 Evaluate using Wallis' Formula: sin5 x cos6 x dx

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Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

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Q: 1) Using the formula: cos(x +y) = cos x cos y – sin x sin y, prove in steps 1+cos 2 x that: cos? x =

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: 1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps that: cos? x = %3D…

A: Note - Since you have posted multiple questions, I am answering first one for you as per the…

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: S(x) - e 05 (2 cos 2.x+3sin 2.x) 7. , evaluated at x 1 rad

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