a) By expanding sin(2x+x) using double angle formulae, show that and sin 3x = 3 sin xr-4sin x. Hence, prove that sin xdr = 24 b) Evaluate (x + )In xdx

Q: If a, B, y, ð are the smallest positive angles in ascending order of magnitude which have their…

A:

Q: 2.) Evaluate using wallis formula 1-x² dx and let x= sine

A: Given ∫01x41-x2dx By using 1-sin2(x)=cos2x And Wallis formula…

Q: (-n *) Prove sin? x – sinx cosx – 2 cos? x =0 in п, 2 has five root's Hint. Intermediate value…

A:

Q: Prove that sin 4A = 4sinA cos³A - 4 cosA sinA.

A:

Q: Show that 2 sin 0 + sin 20 sin 0 1- cos 20 1 cos e Prove that (G) 1 T 1 tan-1 + sin V5 3. where…

A:

Q: (a) Buktikan, Prove that, (sin x + cos x)* = sin" 2x + 2 sin 2x + 1. %3D

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

Q: By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x – 4 sin'x.…

A:

Q: ) Prove that 2+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: 4. sin 20 + cos 0 = 0 on the interval [0, 27) *Hint: use Double Angle Formula

A: sin(2θ)+cos(θ)=0We know that ,…

Q: = Prove, for any angle x, Cos (sin¯' (x)) = /1 – x². %3|

A: Let sin-1x=θ Then, x=sinθ As sinθ=Perpenicular Hypotenuse=x1

Q: Using an appropriate identity, compute the exact value of sin(375°). V3-V2 4 V6-V2 2 V2+v3 4 O v2-1…

A:

Q: Express sin 20 in terms of x, where x = sin 0. A. sin20 = sin? 0 = x² 2x(1– x² )² C.sin20 =…

A:

Q: Find sin 5, given that sin x = 2 i and 0<x<5.

A: Here  sin x=14⇒cos x=1-sin2x              ⇒cos x=1-116              ⇒cos x=154 Now, sin2x2=1- cos x2…

Q: (a) Prove that Sin-1x  + Cos-1 x  = π/2 .(b) Use part (a) to prove Formula 6.

A: a) We have to prove sin-1x+cos-1x=π2 Let sin-1x=θ                                     ⋯⋯1…

Q: 8 and x terminates in guadrant III. 15 Find sin 2x, cos 2x, and tan 2x if tanx= sin 2x %3D cos 2x…

A:

Q: Find the exact length of r = 3 sin 0 + 4 cos 0. II

A:

Q: Q2/Prove that cos 17° + sin17° = tan62° cos17° – sin17°

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

Q: Evaluate using Wallis' Formula: So sin® x cos4 x dx -Tt/2

A:

Q: (b) в — р2'а, + psin'ф а, + 2pz sin' ф а, sin²o as + 2pz sin*ф а,

A: The complete solutions are given below

Q: Hence prove that sin?a + cos²ɑ = 1 3.2

A: Since you have posted more than one question, we solve the first one for you. For the other…

Q: The value of the expression cos z - tan z – 9+ sin z+ secz is

A: given expression is…

Q: V3 Prove that sin 10° sin50° sin 60° sin 70° %3D 16

A: Given, sin10.sin50.sin60.sin70 =sin 60.sin10.sin50.sin70 = [(√3)/2]sin10sin50sin70 =…

Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x - 4 sin°x.…

A: Evaluation of the definite Integral

Q: tan 5, given sin 0: 3 270° <0 < 360° 5

A:

Q: Show that V2 + V2 cos 2 and cos 16 and use it to find sin 16 Show that

A:

Q: Prove that: Sin'x+ cosx=I

A:

Q: Q2/Prove that cos 17° + sin17° = tan62° cos17° - sin17°

A:

Q: Prove 3n - T, 2 sin? x – sinx cosx – 2 cos? x=0 in has five root's Hint. Intermediate value theorem

A: Corollary of Intermediate value theorem :- If a continuous function has values of opposite sign…

Q: Show that given that z = sin-12 дхду дудх

A:

Q: Prove that X + 8 2 TT sin 8 2 1 sin x X sin?

A: We use Trigonometry identities , double angle formulas to prove this Question

Q: 4. Establish the identity using the sum and difference formulas: sin (m – 0) = sin 0

A:

Q: Prove that sin? 0 + cosª 0 = sin“ 0 + cos² 0.

A: Using fundamental identity of trigonometry.

Q: Find a series of cosines of multiples of x which will represent (x sinx ) in the interval (O, x) and…

A: Let's expand x cos(x ) , xcosx=x1-x22!+x44!-x66!+...=x-x32!+x54!-x76!+...             in 0,x To show…

Q: express 5^(1/2) sin 2x + 2cos 2x =1 in the form R sin(2x + y) where R >0 and y is acute angle in…

A: Let's Solve,

Q: (7) (a) Prove the identity using Double Angle and Sum to Product Formulas: sin 10x cos 5x %3D sin 9x…

A:

Q: Prove that, cos20 + sin?0 = 1

A: Let a, b and c be the lengths of right angled triangle. Then by definition,

Q: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function:

Q: Evaluate 2 sin x cos x dx by three methods: (a) Let appearance of the answers obtained in (a), (b),…

A: To evaluate: I=∫2 sin x cos x dx

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

A:

Q: Find all values of sin-V2 Given Z, = -1 + iv3 and Z, = -v3+i, show that In (Z,.Z2) # lnz, + InZ2 %3D

A: (a) We have to find all values of sin-12

Q: what is the exact value using half angles for 1. sin(11pi/12) 2. cos (7pi/8) 3. tan (5pi/12

A:

Q: Q1- Show that cote)+tan(e) a. cofe)-tan(9) sec(20) b. sin(36) = 3 sin(@) - 4sin (0) = Se %3D

A:

Q: -Tt/2 Evaluate using Wallis' Formula: 7 sin5 x cos6 x dx

A:

Q: Suppose that sin(In z) = }, and that sin(In y) = }. If 0 < In z < and 0 < In y < §, use the…

A:

Q: Prove that sin 4A = 4sinA cos³A – 4 cosA sin'A.

A: we have to show that the following

Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: Recall that sin² 0 means (sin 0)². V5 find sin2 0. If sin 0 = 3 %3D sin? 0 = %3D

A:

Q: Find two angles in the interval [0, 360°) such that sin(x) = -0.61566 %3D

A:

Q: Prove Sin (A+B)+Sin (A-B)=2SinA.CosB

A: