Why is V /5+ 5 tan² 0 = v5 sec² 0? Because Vtan 0 = sec 0 Because 1+ tan² 0 = sec² 0. • Because sec? 0 = cos? 0

Q: 4. Establish the identity: sec ar - secr sin2 = cos LIC HS O6Y

A: Establish the identity

Q: Q4:B/Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40]³[cos 20-i sin2015 using De…

A:

Q: 2. y = sec- (6a2 –- 3x + 2) 3. y = (8x – 6) sin (8x – 6) 4. y = cos- (8x - 4)

A: As per the guidelines, I can solve only first 3 parts. Kindly repost for remaining parts

Q: cos 2x +1 sin 2x Prove that Please show proper steps sin 2x 1- cos 2x

A:

Q: tan 0 de equals to : 1+sece In |1+tane|+c In |1+sece|+c O (tane)^2/2+c -In |1+cose|+c

A:

Q: Find the value of x  sin2x=sin600cos300-cos600sin300

A: Given,           sin2x=sin60°cos30°-cos60°sin30°

Q: What is the exact value of 2sin(x/2) * cos(x/2) if sin of x = 3/5 and cos of x = 4/5 ?

A: To determine the exact value of the expression.

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: tan(2x) O 1+ cos(4x) sin(4x) O cos(4x) – 1 sin(4x) O 1- cos(2x) sin(2a) sin(4x) 1+ cos(4x)

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: The suitable substitution to evaluate / sin²4(x +2) dx is (1- cos8(r + 2)] [1+cos8(x+2)] None 1 [1-…

A: We have to find the suitable substitution to evaluate the following integral -  ∫sin24(x+2) dx

Q: 2 (tan²x + 1)√sin2x.dx= (tan², 0

A: Find your answer below

Q: 2

A: Prove: cos²(x/2)=(sin²x)/(2-2cosx)

Q: tan(2x) = O cos(4x) – 1 sin(4x) COS O 1+ cos(4) sin(4x) O 1- cos(2) sin(2x) sin(4x) 1+ cos(4x)

A:

Q: Find sin 2x, cos 2x, and tan 2x if tanx=- 1 and x terminates in quadrant II. sin 2x %3D cos 2x %3D…

A:

Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

A:

Q: Find all solutions of 4sin^2xtanx−tanx= 0 that are in the interval [0,2π)

A: Given the equation  4sin2xtanx-tanx=0. We need to find the solution in the interval [0,2π)

Q: Find tan 0 if sin 0= 1/4 and 0 terminates in Q1

A: Given, θ terminates in Q1 So, tan θ i s positive

Q: how that cos 1+cos 8 and sin 1-Cos 0 %3D %3D using de Moivre's Theorem.

A: It is required to show that cosθ2=1+cosθ2 and sinθ2=1-cosθ2 by using de Moivre's theorem. By de…

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

A: Given expression is   2 sinx -2 cosx

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Describe the thans formation and tan Station by rephesented by the Pquatlon 9= -2.5 Sin (x - 13.4°)…

A: y=-2.5sinx-13.4°-0.6To describe the transformation and translation

Q: Solve 4 tan x * cos^2 x = 1 for 0 ^ 0

A:

Q: tion for sin x= 0.3

A:

Q: tan20 21-25. Verify = sec?e – sec 0 cose + 1

A: To verify: That tan2θcosθ+1=sec2θ-secθ. Formula used: Trigonometry identity: tanθ=sin θcos θ…

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: coS(T/11)-cos(2t/11)+cos(3t/11)-cos(4Tt/11)+cos(5rt/11)=?

A: To determine the value of the below expression. cosπ11−cos2π11+cos3π11−cos4π11+cos5π11

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: y cos?£ 1-CUSE tanzz

A:

Q: Approximate all solutions to tan(x)2 +4 tan(x)– 21=0 in the interval [0°,360°) X = |degrees Round…

A: We have to find

Q: 7. B- Show that: (1) lime-0 tan 8 (2) tan 0 sec20 =D1 %3D do

A: Solve

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: sin(2r) cos(2x) +1 2. Prove: csc(2x) + cot(2r). %3D COS

A:

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: -1 V3 2 Blank 1: CoS Blank 2: tan- (-) 3 (sin (-4)) Blank 3: sec 2 Blank 4: cos- (cos (*)) Blank 5:…

A: We have to find the exact values .

Q: 1 what are possible values of cos x and tanx? 2 If sinx= Select one: V3 and tanx= 2 1 a. cosx= V3 V3…

A: Consider the right triangle with one angle x degree. Let a be the length of the adjacent side and b…

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40³[cos 20-i sin2015 using De…

A: Formula Used-  De Moivre's theorem: cosθ+isinθn=cos nθ+isin nθ cos mθ+isin mθcos nθ+isin nθ=cos…

Q: Suppose that sin(θ)=2/6. What sec(θ)=______.

A: As we know that; The trigonometric ratios;…

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

A:

Q: sec 0 + In + 22+3 = -3 2 In y + 322-4 = 1+ cos 20 2/1+ (tan 0)2 +2ln y+2 3

A:

Q: Use Simpson's rule with n = 4 to approximate /" cos(2) -dr

A: Given: ∫16cosxxdx Here a=1, b=6 and n=4  h=b-an∆x=6-14∆x=54∆x=54

Q: Show that cos(arcsinx) Vi - x², for x| s lin two different ways.

A: Show that cosarcsin(x)=1-x2, for x≤1

Q: 1- cos 4x 9. sec2 2x – 1 = 1+ cos 4x

A:

Q: Recall that sin2 0 means (sin 0)². find sin2 0. If sin 0 = sin< 0 =

A:

Q: Evaluate: | tan(4x + 3)dx i -In |cos (4x+3)|+C A COS 4 В 4 - In |sin (4x + 3)|+C In |csc (4x+3)|+C D…

A: Given: ∫tan(4x+3)dx =∫sin(4x+3)cos(4x+3)dx Substitute :…

Q: do 6) I cos° 0 7 [(1- sin° 31)- cos3t dt 8) | tan (5x)· sec (5x) dx

A: Since you have posted multiple questions we solve first question for you  To get the solution of…

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: sec 1.)S Intanßtanß dß

A:

Q: Suppose that π/2≤θ≤π, sin(θ)=2/9, find cos(θ)=______. (round to 3 decimal places)

A: Here, θ is in the second quadrant( π/2≤θ≤π) and cosine is negative in the second quadrant.