2. Given that csc A = v2, A in QI, and sec B V5, sin B <0, find: a. cos (A- B) b. tan (A- B) %3D

Q: Suppose y = tan x. A. Find dy and Ay when r = 60° and Ar = 1°. B. Use your answer in part A to…

A: Given that y=tanxA. y=tanxdy=sec2xdxdydx=sec2x△y=dydx△x△y=sec2x△x△y=sec260°×1°△y=4×1°=4°

Q: Given that " = n, sin (x) dx 3 -T, what is 8 sin (0) de?

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Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

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Q: implicitly, if e"(e – 1) + sin(2r + 5y) = In(v7) -- cot(2x) Find

A: Implicit functions are thise functuon in which we can't separate variables. We have to difderentiate…

Q: B) 1- Given that a = sin Find cos x, tan x, cot x, secx and csc x ?

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Q: If sin A = with A in QII, find Cos 9 cos Cos COS Cos Cos 스2

A: cos2A +sin2A =1 cos(2A)=2 cos2A -1

Q: + C,? What should be the value of A so that f A : sin (6x²) dx = - cos(5x-) %3D 4 A. x С. Зх В. 2х…

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Q: 2. If tan 0= x2, which of the following is correct? Defend your answer. a. cos 0 = 1/V(1+x^4) b. sin…

A: The solution for the above question is as shown below

Q: At what value(s) of x does cos x = 2x?

A: To determine the intersection value of x where x = 2x.Here the first curve is y = cosx and the…

Q: Suppose sin u=x and u is between 0 and 2. What is cos u? V1- 22

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Q: e Suppose flx) = Sin (x) For which value %3D of a, osas T, will f'la) = 0.

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Q: Find the value of the trig function indicated. 1) tan 0 2) sin 6 7V5 14

A: Solution: The objective is to find the value of sin(θ)

Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: S sec" (0) tan" (0) do is u = tan(0)

A: Evaluate ∫sec10θ tan8θ dθ

Q: 2. If tan 0= x2, which of the following is correct? Defend your answer. a. cos e = 1/V(1+x^4) b. sin…

A: As per the guidelines I can solve only one question

Q: If csc(z) = 6, for 90° <z< 180°, then %3D sin () %3D «(금) cos tan(플) - ||

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Q: If sin (x – -) = A cos x, then the number A is equal to A. π С. О В. Е D. –1

A: Given that sinx-π2=A cos x

Q: ) Use Euler's formulas to calculate | cos(ax) sin(bæ)dx for a > 0 and b > 0.

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Q: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

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Q: Find dr 0Y-- の 3. Cosr+ Cot O =r

A: Solution:-

Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

Q: es (or+.1). COS Using P, (x), eshimate cas

A: In the question it is provided a function fi=cosπ+i The objective is to estimate the above function…

Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: By using u = tan 0, evaluate tan 0 sec*e de.

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Q: On what interval is the solution of the IVP cos e (1+ sin 0) y (0) = 2 - 47 valid?

A: Given IVP is dydθ=1cosθ1+sinθ y0=-12 Now,  dydθ=1cosθ1+sinθ dy=1cosθ1+sinθdθ∫dy=∫1cosθ1+sinθdθ

Q: Using appropriate substitution, ſ sin1º(x)cos³(x)dx is equal to: an

A: By using integration by substitution.

Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: Why does eix=cos cos x + i sin sin x ?

A: To prove , or justify the identity exp(ix)= cosx+isinx

Q: Sec A - cos A is identically equal to

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Q: .... 2. .... 10 .... 50 Show work: trig ratio (sin, cos, or tan) of L = trig ratio: =7°

A: tan 50∘=pq Here, p represents opposite and q represents adjacent. p=x and q=10 Substitute the value…

Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: If  sin⁡x=e^y,  0<x<π, what is dydx in terms of  x?

A: Given sin x = ey   ..................(1) Differentiating both sides with respect to x  d(sinx) / dx…

Q: 16. Determine So sin x cos x dx

A: First simplify then integrate

Q: 16. Complete the following table of signs: ө sin 0 cos e tan 0 cot 0 sec 0 csc e 0 < 0 < <A < : 2 Зл…

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Q: Given that E = sin*x- cos*x. Reducing E in terms of the first power of cosine gives:

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Q: Evaluate 3 cos z sin" e dz.

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Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

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Q: Given that (-) x sin-1 -1 = COS eya. dy in the terms of x and y. dx Find

A: Given: xsin−1⁡1y=cos−1⁡eyx Since, dsin-1xdx=11-x2 and dcos-1xdx=-11-x2

Q: Given tan x = sin x < 0; cos y = csc y < 0, find sin(x-y) 3/5

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Q: Find the exact value of sin​(u​-v) given that sin u= 5/13 and sin v= 8/17​, with u and v in quadrant…

A: In the question we have to find sin(u-v).Where u and v are in first quadrant.

Q: express the given quantity in terms of sin x andcos x. sin (2π - x)

A: expression in cosine and sine form of sin2π-x We used identity:  sinA-B=sinA cosB-cosAsinB

Q: Given cos x sin x < 0; tan y = sec y < 0, find sin(x+y)

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Q: If sec A = V 50 with 0° <A <90°, find sin 2A and sin A/2

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Q: 2. If sin a =,0<a< 3. 2V5 ,where <B < 2n 3 . cos ß = Determine the value of a. sin(a + B)%3D b.…

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Q: y = C, sin at + C2 cos at, (a not to be eliminated)

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Q: Given that the value of sin x – cos x = -1/3, find the numerical value of sin 2x.

A: We have to find

Q: A certain substitution gives S sin*x)cos"(x)dx = S (u²-u*)du .what is n?

A: For substitution- Balancing the above equation, we can solve it as follows-

Q: If the solution of y' = cos x - y sec x passes through the point (0,1), determine y when x = TT…

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Q: Given that sin(a) = and cos(b) 5 with a %3D 4 sin(a + b) = %3D cos(a - b) = %3D

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Q: Given x sin4t, y = -cos4t, then find at t =.

A: x=sin4t   ,y=-cos4t