3. (a) Use the substitution x = 2 tan 0(-1/2 <0 < T/2) in the expression T/V4+x2 and show the result is sin 0 %3D (b) Using appropriate identities, if sec 20 = 3 and -n < 20 <0 find sin 0 and cos e %3D

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A: 1 x2+1-x By rationalization  =x2+1-xx2+1+xx2+1+x=x2+1-x2x2+1+x=1x2+1+x Therefore, as x→+∞ there…

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A: To evaluate the integral.

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

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A: On solving this by doing differentiation implicitly we get

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A: As per our expert guidelines we are allowed to solve only one question. kindly repost others. thank…

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A: Given:- tan(x) =-4/3 To find:- value of sin(2x), cos(2x), tan(2x)

Q: How do you solve this and can you show me step by step?

A: Given equation is

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Q: 2. Write –2 cos x – 3 sin x in the form R cos(x – a) with -7 < a < T. Round to three decimal places.

A: Answer is given in asked form.

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Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

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A: To find out the derivative.

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Q: Evaluate the integrals

A: 71). To evaluate the integral: ∫tan2x+sec2xdx Solution: We know that, sec2θ-tan2θ=1⇒tan2θ=sec2θ-1…

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A: We can solve the given problem as follows:

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A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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Q: b. Express tanh x in terms of e* and e-* and hence show that 2 tanh x tanh 2x = 1+ tanh? x' c. Given…

A: (b) To proof :   tanh2x=2tanhx1+tanh2x It is known that, sinhx=ex-e-x2coshx=ex+e-x2 so,…

Q: 9. Solve the equation for x if 0 < x < 27. 2 cos x + tan x - sec x = 0 VI

A: The correct option is option A. Use the trigonometric ratios and identities to rearrange the given…

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A: Since you have posted a multiple question according to guildlines I will solve first question for…

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A: The objective of the question is determine the integral.

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Q: $5. (i) show that: sin 0+sin 20 = tan 0 1+cos 0+cos 20 (ii)Find the general solution of the equation…

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A: Solve the problem within the domain first find the inverse and then solve.

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A:

Q: 1. Calculate for one real root of tan x = 4x with xo 1.2 %3D up to six decimal places using the…

A: Ques : tanx=4x f(x) = tan(x)-4x f'(x) = sec2(x)-4 x0 = 1.2 By Newton Raphson method xn+1…

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A:

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…

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Q: 2. If x = 2 sec 0 and 0<0< T/2, then %3D (a) sin 0 = (b) cos 0 (c) tan 0 =

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Q: 1 3. a) Verify that sin x cos x = tan x--- π for the value x =-. 4 Ls Sin 4cos 4 2.s TanT/4-Y2 しS…

A: We can use the concept of trignometrical ratio in order to solve the given problem.

Q: The result of solving the integral x' tan(x²) dx is: A) Inlcos(x) +c B) tan(x)-+ In/cos(x²)|+c D) +1

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Q: Where does the periodic function ƒ(x) = 2e^(sin (x/2)) take on its extreme values and what are these…

A: Given,

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

Q: Number 13 part C please :)

A: The given trigonometric equation is

Q: 19. Given 0 <8 < 27, solve tan 0 =-V3. %3D 5x

A: General Solution   tanθ=-3θ =2π3+nπ