Example 10: Find 2. given sin xy = tan?x - sin(x + y) + 37 dy Example 11: Find y= tan x prove that = sec²x dx dy Example 12: Find y= proof that if y = sin x then dx = COS X

Q: tan3x)dx tan Evaluate: cos23x A - In|sec (tan3x)|+C - In|cos (tan3x)| +C B © In cos(tan3x)| +C in…

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Q: tan(tan3x)dx Evaluate: cos-3x -In |sec (tan3x)| + C (B ® - in [cos(tan3x)| + C © - sin( tan3x)| + c…

A: We need to evaluate the following integral I = ∫tantan3xcos23xdx…

Q: If x = 3 sin(0), then а. V9 + x? cos(8) 3 b. cos(x) Vx2 + 9 C. tan(x) d. cot(x) = 3 || е. sec(x) 3 O…

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Q: (a) Find S(tan x)dx (b) Evaluate i sin 3x cos 3x dx d (c) Find (2x sin 2x + cos 2x) and hence…

A: a) ∫tan2πx dxb) ∫π9π6sin3x cos3x dxc) ddx2xsin2x+cos2x and ∫0π4x cos2xdx

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given:

Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

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Q: f/² sin (1) 4x ; (**) sin (²) COS (²) dx (Consider initially the first 2 terms)

A: ∫vn dv =vn+1n+1+C

Q: a) Show that sin¯'x + cosx = 2 E) - tan-' (). x(x-y) y(x+y) (b) Find the value of tan1 where >-1…

A: We can solve these two question by using the properties of inverse trigonometric function as below.

Q: tan( tan3x)dx Evaluate: cos²3x A 3 -In sec(tan3x)| + C B -n|cos( tan3x)| + C In|cos (tan3x)| +C (D D…

A: the given integral,      ∫tan(tan 3x)dxcos23x

Q: 3x 7 If sin x= - 西,1Sx<2 37 and CoS y = 2 evaluate: tan (x+y)

A: Given problem:-

Q: tan 2x sec 2x dx Evaluate cos 2x O 1 ,tan 2x e + C 2 2 e tan 2x + C O -2 e sec 2x + C 1 ,tan 2x + C…

A: ∫etan2x sec2xcos2x dx=∫etan2x sec2x sec2x dx     ∵secx=1cosx=∫etan2x sec22x dx Now put,…

Q: If cos(0) 1 and 0 satisfies T < 0 < , find sin(0). 2 - sin(0) = %3D

A: Given: cos θ=-16 &amp; π&lt; θ&lt;3π2 To determine: sin θ

Q: 1. f/² sin () cos (+) sin (²) d dx (Consider initially the first 2 terms)

A: We have to use the formulas for 2sin(A)cos(B)-sin(A+B)+sin(A-B) and 2sin(A)sin(B)=cos(A-B)-cos(A+B).…

Q: COSX 1+Sinx 1+ SinX CoSX (2) See (mx) tan(inx) e a-be

A:

Q: tan x-7 3. Differentiate. y = secx Select the correct answer. dy bl dx a) = 7 cos x + sin x = cos x…

A: Note that derivative of sinx is cosx and derivative of cosx is -sinx

Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

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Q: a Exercise: If L{sin (ax)} = p2+a2 then find L{x sin (ax)}. %3D Exercise: If L{cos(ax)} = p2+a2 then…

A: Since you have not mentioned the number of questions. I am just doing the first two questions. If…

Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

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Q: Please find all 0 ≤ 0 ≤ 2π, for which ... (a) tan () = √3 (b) 3 sin²(0)+ 4 = 5 (c) 2 cos(ln(x² + e²)…

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Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: 4. What is (Cos (x²)} dv 5. What is (tan x³) dx 6. What is (In x)7 dx

A: To find out the derivative.

Q: COS x (5) dx (1+ sin x)5

A: ∫cosx(1+sinx)5dx

Q: Evaluate the integrals

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

Q: 3 + cos 3x dx Evaluate sin 3x

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Q: tan x 4. a) Evaluate dx. In (cos x) b) Evaluatef e4*x3 dx.

A:

Q: Suppose: sin(x) = -0.1 cos(y) = 0.5 tan(z) = -4.3 Then, sin(-r) =| 0.1 cos(-y) = 0.5 tan(-2) = 4.3…

A:

Q: 1+ sin 0 . Verify cos O 2 sec e Cos A 1+ sin A

A: Our Aim is to verify 1+sin θcos θ+cos θ1+sin θ=2 sec θ -(i)

Q: 9. y = -sin (3x) 10. y = tan (x - 60) 11. y = cos (x + 30) 12. y = 3 cos (2x)

A: In both cases there is translation of graph.

Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

A:

Q: 1. у %3D х3 — х?cosx + 2xsic 2 sin x – 1 2. у%3D cosx+ 2 3. tan(xy) + xу %3D 0 4. у %3D хсоsх

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Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: 6 (A) /₁ √== B)/ -x/4 D) dx = tan* (x) sec²(x) dx = C) [rea *² x² ex dx = E) 2x cosh(x²) dx = F) /…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first question. If you…

Q: Show that y = sin x, y = cos x, and y = a cos x + b sin x (aand b constants) all satisfy the…

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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: If csc(x) = 3, for 90° < x < 180°, then sin() V2 1 V6 2 COS 2 V3+2v2 V6 V 2 - 1 tan 2 V 3 + 2v2

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Q: 1) B = cos 30 + sin² 0 tan 2x 2) y = 1-cot 2x 3) w = 2 csc(1 – 3x)

A: This question is taken from the derivative in which we have to find the derivative of the given…

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: 1/2 sin? x + sec² x ) dx (1+ cosx)²

A: To find the integral of ∫0π/2sin2 x1+cos x2 + sec2 x dx Let us first simplify the integrand, sin2…

Q: 1. Solve the DE: tan xsin y y'+(3 tan x-2 cos y) secx= 0

A: Given tanxsinyy'+3tanx-2cosysec2x =0 tanxsinydydx+3tanx-2cosysec2x =0 3tanx-2cosysec2xdx+tanxsinydy…

Q: Find: 2 Sin /2 t - 3 Sin t t – 2.Arc tan- + 3.Ac tan s - 2 Arc tan - 2 3.Ac tan s A.) В.) - 2.Arc…

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Q: Test for exactness then solve. (cos x cos y − cot x)dx − (sin x sin y )dy = 0

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Q: 3. y³x2 – cos- sin x² + esin x = 1 y DIFFERENTIATE THE GIVEN

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Q: tan( tan3x) dx Evaluate: cos²3x A - In|sec ( tan3x)|+C 3 B -In|cos( tan3x)|+C В 3 © In|cos(…

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Q: Problem 1. (a) Show that that 1 – tanh² x = sech² x and use it to prove that sech(tanh x) = v1 – x².

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: ll solutions of the equation in the interva tan(x + T) + 2 sin(x + t) = 0

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Q: */2 2 cosx dx 1+ (sin x)2 -n/2

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Q: 1+cos 2x dx sin 2z O cot 2x - csc 2x + c O cot 2z +In |sin 2z|+ c O none of these O In (csc 2x + cot…

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

A: Given inequality does not equal. See the attachment

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.