Prove the identity. sin(x + y) – sin(x – y) - tan(y) cos(x + y) + cos(x - y) Use the Addition and Subtraction Formulas, and then simplify. )- (sin(x) cos(y) - cos(x) sin(y) sin(x + y) – sin(x - y) cos(x + y) + cos(x - y) (cos(x) cos(y) – sin(x) sin(y) + (cos(x) cos(y) + sin(x) sin(y) 2 cos(x) cos(y) 14 cos(y)

Q: The value of cos x is given. Find sin x and tan x if x lies in the specified interval. cos x 3n CoS…

A: Given:  cos x=-45, x∈π, 3π2 To Find:  To find sin x and tan x for the specified interval.

Q: sin(z² -2z–3) Identify and remove, if possible, discontinuities of f( x) = %3D tan(z² –2z–3)* O…

A: A function is said to be discontinuous if the limit does not exist

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: Prove the identity. cos(x-y) / cosx cosy = 1+tanx tany

A: To Prove:cosx-ycosxcosy=1+tanxtany

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

A:

Q: 1- cos x The lim X40 sin x is equal to O 2 Zero O-

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: (÷++) + co« (5 - ). cos 3 x ) is equivalent to O cos 2x cos x O sin x cos x

A:

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: 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: Prove the identity. tan(x -)- -cot(x) TC tan x 2 %3D sin(x - ) | tar(x-)- sin(x) cos) - cos(x) sin…

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: Using appropriate substitution 3. tan’x dx sec5x is equal to -cos°x + cos"x + C tan*x + 6 sec°x + C…

A:

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: Choosing between A B or C HW 12

A: We know that,

Q: cos² (1 – cos?(1 – cos² (1...cos² 0)).....) cos“ (1...cos´ 0)).....) - - Evaluate lim TT (/0 + 4 sin…

A: Introduction :

Q: Verify the identity. 1 + sin 2x cos x+ sin x %3D cos 2x cos x- sin x Choose the sequence of steps…

A: Sin2x correct formula is- Sin2x=2SinxCosx So this formula is only used in option 2

Q: 9. Prove each identity. cos 0 COS sin 0 = 1 – tan 6 a) cos² 0 + sin 0 cos 0 %3D b) tan? x – sin?…

A: we have to prove the given identities

Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

A:

Q: tan(x) dx cos4(x) tan'(x) A [7tan²(x) +9] + C 36 1 ℗tan'(x) + tan³(x) + C C D sin²(x)sec³(x)…

A:

Q: sin x= 6/7, cos > 0, sin y = -1/5, and cos y < 0 How do I find sin(x + y), cos(x + y), and tan(x +…

A: Given that  sinx=67, cosx&gt;0,siny=-15and cosy&lt;0. We know that…

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: Prove the identity. 4 sin(x - y) cos(x) cos(y) 4 tan(x) - 4 tan(y) Use a Reciprocal Identity, and…

A:

Q: tan (x) J Cos cos“(x) 하an7(x) + 늑tan®(w) +C O tan'(x)7tan?(x) +9]+ C tan7(x) 36 O sin…

A: Here we have to integrate the given function.

Q: Prove the identity. 1 + tanh(x) – e2x 1 - tanh(x) 1 + cosh(x) 1 + tanh(x) 1- tanh(x) 1 - cosh(x)…

A:

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

A:

Q: 1. 1-Cos? X= tan x cos x sin x 2. cos x tan3 x= sin x tan? x

A:

Q: Verify the identity (1+sin x)(1-sin x)=cos2x   (sin x + cos x)2 + (sin x - cos x)2=2   cot(x) =…

A: (1+sin x)(1-sin x)=cos2x Apply FOIL method to expand left side

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: sin 0 13. Prove that 1 - = Csc 0(1 + cos 0). Cos 0

A:

Q: X+1 1-x Select one: a. sin-1(x)-V1-x² +c www. O b. sec-(x)-V1-x? + c C. tan (x)-V1-x2 + C d. cos x)…

A:

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: lim,-o-cos(2.x) →0°sin²(3x) Q6- Evaluate:

A:

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

A:

Q: 6(cos² x – 1) sin a cos x – sin x O 6 sin æ + 6 cos e O 6 tan x + 6 sec x O 6 tanx +6 csc x O 6 cot…

A: We need to simplify the following expression 6cos2x-1sinxcosx-sinx

Q: x(1+x?) sin x+ cos x + x² cos x – x cos x (1+ x³)% = (1+x?)?[cos x– x(1+x?)sin x]

A: We want to prove that both equation are equal.

Q: (a). Find a common denominator for COSX |- COSX and 1- COS x COS x –COS X COSX = cosx-coseX COS X…

A: a To find a common denominator for 1cos x and cos x1-cos x.b To expand cos x+tan x2 and to simplify.

Q: 1+2 sin x cos x 1-2 cos2 x sin x+cos x (d). sin x-coS x | |

A:

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: 1. Evaluate 2. Evaluate sin(20) 30 x-2x cos x sin x limo lim, 0

A: Given is  limθ→0sin(2θ)3θ. L'Hospital rule: limx→af(x)g(x)=limx→af'(x)g'(x) NOTE: According to the…

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: Verify the identity. sin (e + n) = -sin e A) sin (e+x) = cos Osin e- cosa sin a = cos Osin e--0 =…

A:

Q: 5. y = tan-¹tan x] ab 6. f(x) = x² cos-¹¹-√x²-1 7. f(x) = tan ¹(sin² (2x)) 8. y = (cot ¹(sin¹(x))³

A:

Q: Verify the identity. 1+ sin(x) = (tan(x) + sec(x))² 1+ sin(x) 1 - sin(x) 1- sin(x) 1+ sin(x). 1 +…

A: