22. Fill in the blanks: (a) sin-x is the angle in the interval is x. (b) y = arcsinx if and only if siny = _, for all x €_ and y e . (c) If tan-1x = 0 and tan e is positive, then e is in the whose quadrant. (d) If arctanx = 0 and sin 0 = , then cos e

Q: Eliminate n from their equations  X= sin n + tan n and y=sin n - tan n

A: With the help of trigonometric identities we eliminate n from the equations.

Q: Suppose y = sina, which is TRUE about y? 1 Oy= sin O none of the above y 0 *= arcsing O * = sin y

A:

Q: 4. Evaluate sin (x) cos°(x)dx

A: To evaluate the integral

Q: lim, 0 tan² (7x) cot(11x) (r+7)sinx

A: Given: The limit as limx→0tan27xcot11xx+72sin x. To find: The main aim is to find the value of the…

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A: Formula used is written in the bracket of the first photo.

Q: 2. (a) Find the tangent line approximation to sin(x) near r 0. (b) Is the tangent line approximation…

A:

Q: Prove a (cosa + cosß) + (sina + sinß) = 4cos² (@ - B) 2 %3D

A:

Q: Where does sin x have a horizontal tangent line? Where does cos xhave a value of zero? Explain the…

A: Concept: The function f(x) at the point x=a, is a line that just touches the graph of the function…

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A: (i) Consider the provided information, sin-1sinπ3=π3 Prove that left hand side is equal to right…

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A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: (-등, 풍) satisfying TT Find all values of 0 in the interval 2 2 2 the equation (1 – tan 0)(1 + tan 0)…

A:

Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

A:

Q: Q/ ind dy if 24-sini' (xe!)=sin'(x*)+ cos (x")

A: Given that      2y - sin-1(x2+1) = sin2(x4) + cos2(x4) Here we have to find dy/dx.

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A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

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A: given,        cosx1-sinx=secx+tanx

Q: Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

A: To verify the identity, sinx+y-sinx-y=2cosxsiny

Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x - 4 sin°x.…

A: Evaluation of the definite Integral

Q: Evaluate (tan x cos x) dx А. cos x + C cos x + C - С. - sin x + C D. sin x + C B.

A:

Q: Find the exact value of sin(x - y) if sin x = 3 ≤ y ≤ 2. on ≤x≤ and sin y=-3 on

A:

Q: one of sin x, cos x, and tan x is given. Find the othertwo if x lies in the specified interval.

A: It is given that sinx=35.

Q: If 1, = | x" sin x dx, prove that 1, = nx"-! evaluate -1,. sin x- x" cosx– n(n-1)I, 2. Hence, = NX…

A:

Q: Establish each identity given in attachment.

A: To establish the identity: lntanθ=lnsinθ-lncosθ Solution: We know that, tanθ=sinθcosθ Property of…

Q: If sinh x =tan t, 0<t<3/2 , then tanh x = sin t. Select one: O True O False

A: We have been given  sinh x= tan t for 0&lt;t&lt;3/2

Q: 7. B- Show that: (1) lime-0 tan 8 (2) tan 0 sec20 =D1 %3D do

A: Solve

Q: 2. Describe a way of evaluating sin° x dx.

A:

Q: An appropriate trigonometric substitution 1 -dx is V4 – x² for x = 2 tan(8) for 0 E (-5,5) а. b. x =…

A: The given integral is: ∫14-x2dx

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A:

Q: ≤ Lºin( Verify that f(x) = sin() is an odd function and use that fact to show that 0 < sin(√√x) dx ≤…

A:

Q: The integartion of [sin(sinØ)]Ø cos dø Is: cos(sin0)+C -sin(cos Ø) + C O -sin(sinØ) + C O -cos(sinØ)…

A:

Q: ind sin2x, cos 2x, and tan 2.x if tanx = -2 and x terminates in guadrant II. %3D sin 2x ? cos 2x tan…

A: In second quadrant sin is positive and cos &amp; tan are negative.

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)

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A: We can answer first question among which you asked as per the honor policy. please resubmit the…

Q: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

A:

Q: Find sin 0 and tan 0 if the terminal side of 0 lies along the line y = 40 in quadrant I. %3D 4/17…

A: Answer

Q: 5) prove that = sin 'x +e using method of trigonometric substitution.

A: To Prove- Prove that ∫dx1 - x2 = sin-1x + c using method of trigonometric substitution.

Q: one of sin x, cos x, and tan x is given. Find the othertwo if x lies in the specified interval.

A: Given sinx=-12, where x∈π,3π2. Since, x lies in third quadrant, so cosine function will be negative…

Q: 1. Given tanx = - and cos x >0, find secx. A. в. C. V10 D. 2V10 2. Given secx and sin x 0. 3. Find…

A:

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -pai to x =…

A: given

Q: Show that tan(arccosx) for |x| s 1, x + 0.

A:

Q: Cos x [SND] If y = tan x+ seç show that, y = (1 – sin æ)?

A: Topic  =trigonometry

Q: ´ tan²2x dx, a = tan" (2)

A:

Q: Determine the concavity of y = 3 + sin x on [0, 27

A: Given that y=3+sinx on 0,2πTo find : concavity of function Solution : if y''=d2ydx2&gt;0 then…

Q: (3) Prove that Sina cos a -Sinß cos B sin cos B sinß cosy sin(2+ B+y)

A: We have have to solve given problem:

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A:

Q: If y=a cos ( sin x) +b sin (sin x :) then y" + (tan x )y'+ cos'x = 0.

A:

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

A:

Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment