Prove the identity. sin(x + y) – sin(x – y) = 2 cos(x) sin(y) Use the Sum and Difference Identities for Sine, and then simplify. x ) sin(x + y) – sin(x – y) = sin(x) cos(y) + cos(x) sin(y) – (sin(x) cos(y) – sin(x)cos(y) ) × 2 cos(x)sin(y)

Q: 2. Prove the identity: (cos x- sin x)2 + (cos x + sin x)2 = 2. %3D

A: To prove  that cosx-sinx2+cosx+sinx2=2

Q: sin? x 1- 1-cos x =-COS X

A: Here we have to use the basic trigonometric identity sin2θ+cos2θ =1 and we know that  a2-b2=…

Q: Express cos- (a) in terms of cos(2a). Express sin (a) in terms of cos(2a).

A: This question is of double angled identity.

Q: 11. Prove the identity sin x 1+ cos x 2 csc x 1+ cos x sin x

A:

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

A:

Q: 3 sin° x -dx Evaluate ' cos° x

A:

Q: Verify the identity:

A: Our Aim is to verify the identity given below:-sin 3π2-x=-cos (x)  -(i)

Q: True or False sin² 0 = 1 – cos² 0.

A: Use the trigonometric identity sin2θ+cos2θ=1 to verify the statement.

Q: V1+x2-V1-x² -1 If tan 1+x +V1-x² =a, then prove that x2= sin 2 a. %3D

A: Introduction :

Q: (ii) Prove the identity (2 - 2 cos 0)(sin 0 + sin 20 + sin 30) -(cos 40 - 1) sin 0 + sin 40 (cos 0 –…

A: Prove the Identity: 2-2cosθsinθ+sin2θ+sin3θ=-cos4θ-1sinθ+sin4θcosθ-1 NOTE: Since you have asked…

Q: Establish the identity. sin x- sin y x+y cot 2 COS X- COs y Which of the choices shows the key steps…

A: To prove the following trignometric identity:

Q: proof 1)  (sin x + cos x)2 = 1+ 2 . sinx . cosx 2)  cos4x - sin4x = cos2x - sinn2x

A:

Q: 5. Verify the identity: sin(x- y)cos y+cos(x– y)sin y = sin x

A: Explanation of the solution is given below.....

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…

A:

Q: Prove the identity: cos(x + y)cos(x – y) = cos?x – sin²y

A:

Q: Verify the identity. cos(4x) = 1 - 8 sin?(x) + 8 sin“(x) cos(4x) = 1 - 2 sin?(2x) = 1 - 2(2 sin(x)·…

A:

Q: sin 0 If 1+cos 0 x2 x2, then tan 2 - a) b) 4 c) x2 + 1 d) x2 |3| 2.

A: Given,  sin θ1+cos θ=x2 To determine tanθ2

Q: What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x +…

A:

Q: Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x…

A:

Q: 5. cos A =- and sin B =, both A and B in QIl. 6. cos A = - and cos B = - 2, with A and B in QIII. 17

A:

Q: Express cos (a) in terms of cos(2a). Express sin (a) in terms of cos(2a). cos (a) Choose... sin (a)…

A: Trigonometric formulas

Q: cos(x1)=-1/3 sin(x2)=2/3 find 1. sin(x1+x2) 2. cos(x1+x2) 3.sin(x1-x2) 4.cos(x1-x2)

A:

Q: sin(2x) 1 Prove the following identity: cos(2x) - 1 - tan(x) sin(2x) %3D cos(2z) - 1

A:

Q: sin (x) = -0.9. If x and y are complementary, what is cos (y)? %3D Sub

A:

Q: Verify the identity. cos(e) sin(0) - csc(0) 1- sin(0) cos(0) - cot(0) sin(e) – sin(0) sin(e) –…

A:

Q: cos 2r Verify the identity: = cos x + sin x. sin x cos X

A: Verify the following: cos 2xcos x-sin x=cos x+sin x

Q: 1- cos e sin 0 sin 0 1- cos 0 23.

A:

Q: 2. Prove the identity: cos (x-y)– cos (x+y) = 2 sinx siny

A:

Q: Prove the identity: sin(0)-co sin (0) +cos (0)–1 cos (8)+1 sin(0)+1 cos(8)

A: On proving this we will get

Q: f2(x) = (4x + 5)°, f3(x) = (2x² + x)/x, fa(x) = cos(3x) – 2 sin² x,

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: 6. The value of A. sin ¹¹x + √1 + x² + C B. sin-¹ x - √1 + x² +C C. sin-¹ x + √√1- x² +C D. sin…

A:

Q: Prove identity: 4 sin x cos x (1 – 2 sin? x) = sin(4x)

A:

Q: 5. Prove the identity. csc 0- cot 0 sin- 2 2 csc e

A:

Q: cos e sin 0 for some real value of 0, and let B= -1 Let A = Consider x - sin 0 cos 0 Then ||(AB)x||…

A: Given,            A=cosθsinθ-sinθcosθ , B=0-1-10 , x=12To find : ABx

Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?   −2   1   2   −1

A: We have to find

Q: 1+ sin 0 cot e Prove : 1- sin 0 (cos ece – 1}

A: Given:                            1+sin θ1-sin θ=cot2θcosec θ-12 Solve left hand side:…

Q: sin 0(3sin? 0+ 4cos? 0) = 3 cos 0 + cos³ 0 4. Prove that tan 0

A:

Q: 3) [~x cos² (x3/2 - 8) dx , A)sin (x/2 - 8) + C 1 = x3/2 – 8 3) 1 B) a32 - 8) + sin 2432 - 8) • C D)…

A:

Q: 2. Show that: (i) sin (ii) A" cos (a + bx) = [2 sin bx + n cos - sin b (iii) A cot (a + br) = sin (a…

A:

Q: CoS X Which of these is an efficient first step in proving the identity 1+ sin x 1- sin x :? cos X

A: To prove cos x1+sin x=1-sin xcos x

Q: Prove the identity. 3 sin(x – y) cos y cos x 3 tan x - 3 tan y

A: Given that  3tanx-3tany=3sin(x-y)cosycosx We need to verify the given identity.

Q: tx)+ Sin(꼴-)- -26S X %3D Prove sin

A:

Q: Ca) Prove that sin-z = -i ln(iz + (1 – z²)/²). ) Find the principal value of sin (2i) and write your…

A:

Q: tanº(x) cos“(x) O sin'(x)sec°(x)[7sin?(x) + 9cos²(x)] + C 63 tanʼ(x) [7tan²(x) + 9]+c 36

A: The properties to be used for solving the integral are: a) 1/cos4(x)=sec4(x) b) d(tanx)dx=sec2x c)…

Q: Write the expression as an algebraic expressionin x for x>0. a.  sec [sin-1 (x/sqroot(x2+9))]

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: sin(3x)cos(3x) sin(2x) 의[cos(2x)-1]+ +C 12 8 4

A:

Q: x) - 0.5 cos(x)) on the

A: Given as, f(x)=e-x3.2sinx-0.5cosx in the interval [3, 4].