2cosx dx 5- f 1+(sinx)2 a)2 tan sinx| b) 2 In sinx| c)2 In(1+ (sinx)1

Q: 2cos(2x)sin(2x)-sin(2x)=0

A:

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

A:

Q: 4. Verify. COSX 1+sinx = 2secx %D а. 1+sinx COSX b. cosx(1+ tanx)² = secx + 2sinx %3D

A:

Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: 5)Prove that (1+sinx)(1+sin(-x)) = cos²x (manipulate left side in order to get right side) %3D

A: We have to prove the given identity: 1+sin x1+sin -x=cos2 x We know that sin -x=-sin…

Q: find integral tan 5 x sec 7 x dx

A:

Q: What is the integrable form of sin-cos-sin@ de? 2 2 sinu du cosu du

A:

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: 1/tanx+secx=cosx/sinx+1  verify

A: We simplify the left-hand side first. Multiplying by (secx-tanx) in numerator and denominator.

Q: (cose+ tane) de / (sece + tan@sec2e) de cos e COS True (B) False

A: We have to find out

Q: What is the integral of (2 sec^2x - sinx) dx? * O 2 cosx+tanx + C 2 tanx + sinx + C 2 tanx + cosx+C…

A:

Q: Evaluate sin 2x sin 4.xdx 2 b. sin 3 2x + C 3 1 a. sin ' 2x+C 3 c. cos' 2x+C 1 с. 3 d. -cos 2x +С 2

A: To evaluate the given integral: ∫sin 2x sin 4x dx

Q: Show that Cosx dx 9- Sin 3D

A:

Q: 2- tan²x + 1 + tanx secx = 1+sinx cos²x

A: To show that , tan2x+1+tanx.secx=1+sinxcos2x

Q: f y=sin(sinx) show that y'' +(tanx) y''+y cos2x=

A: Given that y=sinsinx To show that y''+tanxy'+ycos2x=0

Q: f(t) = In Itsinx 1-sin x g(x) = x sin ¹3x + √1-9x² G(x) = x In (9 + x²) + 6 tan-¹ (-)-2x

A: Note: Since, in the first function there is a typing error "f(t)", it should be "f(x)" because it is…

Q: Express 2 sinx- v2 cos x in the form of Rsin(x – a), w

A: Given expression is   2 sinx -2 cosx

Q: Show that 3(sinx-cosx)*+6(sinx + cosx) +4 (sin r+cosx) = 13

A: Since multiple questions are asked, Answering first one. Repost with other question if you want to…

Q: 7/4 (sec² x – sin x)dx

A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

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

A:

Q: Using suitable method, show that 2 tan" (x+2) dx =- – In 2 .

A: We use integration by parts to find integral tan inverse x.

Q: If () Z = tan || then 2z sin x 1+ z2

A:

Q: cos 2x+1 sin 2.x 7. Prove that sin 2x 1-cos 2x

A: The trigonometric of an acute angle in a right triangle express the relationship between the angle…

Q: (i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in…

A: Trigonometric equation

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

Q: What is the integral of (2 sec^2x - sinx) dx? * 2 tanx + cosx + C 2 cosx + tanx + C 2 sinx + cosx +…

A: Explanation: Given that: ∫2sec2x-sinxdx Concept used: ∫sec2xdx=tanx+C∫sinx       =-cosx+C

Q: x sin 2x sin COSX 8. Prove that: %3D 2x-7

A:

Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: sinx secx + 1 %3D 1 cosx tanx

A:

Q: x where 3π/2 ≤ x ≤ 2π. 1 + sec²x = 2 + cos²x + sin²x

A: Here we use formula of trigonometric equation.

Q: prove that catX+c - Cos'x+Sin2X

A:

Q: Compute (sin (x)) dx cos'x 3 sin' x cos x O Not listed here 3 sin? x 3 sin x cos x

A: Given query is to find the derivative of the expression.

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

A:

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A:

Q: Integral of tan^5(x) dx Show Complete solution

A: This is a problem of differentiation. By general formula we will solve the question. Assume, secx =…

Q: Prove (secx+tanx)/(secx-tanx) = (1+2sinx+sin^2x)/cos^2x

A: To prove that   (secx+tanx)/(secx-tanx) =(1+2sinx+sin2x)/cos2x

Q: Show that sin²(x) cos(x) = sec(x) – cos(x)

A: We need to show the following. So,         Manipulating right side=secx-cosx=1-cos2xcosx=sin2xcosx

Q: 2 (In(sinx+V(sinx)²+1 ))´ d x (sinx)2

A: Let f(x)=(ln(sinx+sin2x+1))2(sinx)2, x∈0,π2 Now,…

Q: Show that n/2 sin x dx sin x + coS X %3D 4

A:

Q: find the area of the shaded 4) reglon y = 2 2- y = 2 sin(Tx) 3 х -1- -2+ -3+

A: From the given graph the shaded part is on the interval x=0.5 to 2.5.  So find the area between the…

Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

A:

Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

A:

Q: Show that:- tan-1 x + tan-1 y = tan-1 x+y 1-ху

A: We need to show the following identity tan-1x + tan-1y = tan-1x+y1-xy

Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

A: