3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of t, where t= tan-

Q: Q2) 1- Find for: y= cos (x)+cos(x*) CoS

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Q: s nip

A: Given: 12cos2x+C=14cos2x

Q: 5. In AABC, m2B = 90°. sin A = 2x + 1.5 and cos C = 3x – 0.9. Find x.

A: Given: In Triangle ABC∠B=90οsinA=2x+1.5cosC=3x−0.9x=?

Q: If f(x)= 3ax tanx + b In(cosx) and f'(x)= 10tanx +9xsec?x, then the values of the constants a and b…

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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: Find the exact solutions of the following equation on the interval 0 sx < 2n: cos (2x) =1- 3sin x

A: Here we have to find the exact solutions of the equation cos(2x)= 1- 3sinx .

Q: Find the value of the number C: 1/2 cos2 x + C = - 1/4 cos(2x)

A: The given expression is12cos2x + C = -14cos(2x)       ......(1)We know that cos(2x) = 2cos2x-1.…

Q: given f (x) = 3/5 cos (6x), what is the smallest possible value for f (x)?

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Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: Refer to the graph of y = sin x or y = cos x to find the exact values of x in the interval [0, 4p]…

A: We have to refer to the graph of y = sin x or y = cos x Then we will find the exact values of x in…

Q: In the process of calculating that: cos³ (112) de a substitution is made in the variable u, then it…

A: Given query is to find the integral after substitution.

Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

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Q: Use the Substitution Rule to provethat∫cos2ax dx =(x/2) +(sin(2ax)/4a) + C.

A: The given integral is ∫cos2axdx=x2+sin2ax4a+C

Q: Ex2: Use the identities 4 and 5 to prove that: cos(x- y)-cos(x+y) (a) sin x sin y = 2

A: Formula used -  cos(A-B) = cosA cosB + sinA sinB  cos (A+B) = cosA cosB - sinA sinB

Q: 1. Determine the value of cos(2x+2y) if sin z 3 and tan y = - for 4 sysa. for 0sxs: VI VI

A: Given : sin x = 3/5 and tan y = -3/4

Q: 4. Derive error-bound formulas for the following expressions. i) cos(x) – sin(x) ii) In(x) + sin-1 y…

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Q: The amplitude A and period T of f(x)=5sin(4x) are..................... and ....................

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Q: DIFFERENTIATE THE GIVEN y = x² co sec™ 3 -1 * COS

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Q: Assume sin(t) = -12 where π < t <3. Compute the following: csc (-t) = cos(t + 2) = tan(t) =

A: We have given  Sint = -1/12 , where π&lt;t&lt;3π/2  Compute  1) cosec(-t)  2) cos(t+π/2)  3)…

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0…

A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx-

A: To evaluate we first multiply and divide by 2 the given function.  Then use the formula: 2(sin(mx)…

Q: The integral So (cos(3x))² sin(3x)dx under the change of variable u = cos3x becomes - ov 29 9/29 u?…

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Q: Which option equalsS x sec2x dx ? Exactly one option must be correct x secx tanx - In(cosx) + C O x…

A: Hence option (b) is correct.

Q: 4) Find when y? – x² + cos(x + y) = 0

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Q: Solve the following for 0 s x s 2n. cotx cos² x = 2cotx

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Q: for what value of x is cosx 1=5cosx is true

A: Solution: Consider the given equation: cos x .1 = 5 cos x Therefore, 5 cos x = cos x5 cos x - cos x…

Q: Q3/ Determine: (a) sin(t) .8(2t – 1) (b) (cos nt). 8(t- 1)dt 8(t –

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

Q: Determine the value of the serie 4∑ ((-1)^n)/(n^2) *cos(nx) at the point x=1

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Q: (5) Use the Intermediate Value Theorem to prove that xe* = cos(x) has a solution.

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Q: Refer to the graph of y = sin x or y = cos x to find the exact values of x in the interval [0, 4p]…

A: Consider the given equation as cosx=-12

Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

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Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

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Q: Find the value of k if 1 х cos(3x) dx 1 3* x sin(3x) + — сos (3x) + C. k

A: .1. ʃ (u.v)dx= u ʃv.dx - ʃ(d/dx(u) . ʃv.dx)dx       Where u and v are function of x 2. ʃ sin(ax) dx=…

Q: Q5-Find2 for + cos(xy) y

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Q: Find all values in the interval [0°,360°) that have the given function value. cos 0 = 2

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Q: Find all solutions to 2 cos(0) - V3 on the interval 0 < 0 < 2n -

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Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) b) y = sin(20) - 2…

A: Differentiate the following  a) y=-cos2x b) y=sin2θ-2cos2θ c) fθ=-π2sin2θ-π

Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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Q: Prove that : n/2 1 dx (a'sin'x + b’cos'x 4a°b³

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Q: -3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0 <a<2n. Express

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: 8. Evaluate (a). (20-0y di (b). / COS I sin(sin x) dx -3

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Q: : s ech[In cosx]tanx dx Evaluate: A None - 2 tan-1(cosx) + C 2 tan -1(e cosx) + C CoSx (D - 2 tan…

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Q: Find cos (0 + p) given that cos 0 = and cos p = and that 0 and p are %3D between 0 and n/2.

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Q: Write 4 coS x sin x in the form R cos(x – a) with -T < a < T. Round to three decimal places.

A: Consider the given function.

Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: O Find the solutions of : 1+sinx=2(cosx)´ in the interval 0<x<2T.

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.