Express sin(x +y+z) in terms of cosine and sines of x, y, z.

Q: i) Sin 20easoal-Sin?

A: Use the trigonometric identities,…

Q: Show that sin-1 v + cos-1 v = π/2 .

A: Given: sin-1 v+cos-1 v=π2

Q: Integrate using u substitution and table    cos2x/(5sin2x-sin^2(2X)^1/2

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Q: Find SinZx, Lo52x, Tan2x Cosxニーニ 3. and X terminates in quadrant 2 Sin2x = Cos 2x = tan 2x =

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Q: How would this parametric function of x=2cost +cos2t; y=2sint-sin2t be solved

A: In order to solve a parametric equation, firstly differentiate x and y with respect to t and then…

Q: Calculate 7² ( sin³ r) dx /2

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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: Express sin 5x cos 3x as a sum of trigonometric functions.

A: Given           sin 5x cos 3x

Q: By using Cauchy laws find: sin (2) dz -i2 cos (2) dz 2-T3

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Q: simplify sin 2x/1-cosx   Not sin^2x its sin2x

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Q: a) Buktikan, Prove that, (sin x + cosx)* = sin 2x + 2 sin 2x +1.

A: The given equation,sinx+cosx4=sin22x+2 sin2x+1

Q: Where are the theta valuss for the horizontal and vertical tangent lines on [0,2pi) of r=1+cos theta

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Q: Prove this equation (cosx-sinx) ^2=1-2sinxcosx

A: Trigonometric formula

Q: Prove a (cosa + cosß) + (sina + sinß) = 4cos² (@ - B) 2 %3D

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Q: Show that cosh iθ = cos θ,

A: We know that  coshx=ex+e-x2 and by Euler's theorem, eix=cosx+isinxe-ix=cos-x+isin-x=cosx-isinx We…

Q: express sin(x+y+z) in terms of cosine and sines of x, y and z

A: Answer and explanation is given below..

Q: Find Lte " sin 41]. -2r

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Q: Show that Cosx dx 9- Sin 3D

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Q: Describe the technique for finding ∫ sec5 x tan7 x dx. Do not integrate.

A: Given ∫sec5x tan7x dx

Q: sin(2x) 2+ cos(2z) da ++

A:

Q: Find the first and second derivatives of r = [3 cos 2t, 3 sin 2t , 4t].

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Q: Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

A: To verify the identity, sinx+y-sinx-y=2cosxsiny

Q: Express the product sin 7x cos 3x as a sum or difference.

A: Given information: The given expression is sin7xcos3x. Concept used: 2sinAsinB=sinA+B+sinA-B…

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: Prove + cosß)* +(sina + sinß) = 4cos² a - B) %3D

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

A: In question We have given two identities and we'll prove it, (i). Cos(π + x) = - Cosx  (ii). Cosx…

Q: Integrate sin (2a)cos (2a)da OS

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Q: Estimate sin 61◦ − sin 60◦ using the Linear Approximation. Hint: Express∆θ in radians.

A: Consider the given trigonometric expression sin61°-sin60° Suppose the linear approximation for the…

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

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Q: Sz sin2m-10 cos2n-10 —— В (т, п) 2

A: It is known that, βm,n=∫01xm-11-xn-1dx

Q: Express sin 2θ in terms of x = sin θ.

A:

Q: 2. Describe a way of evaluating sin° x dx.

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Q: Prove that sin3x/sinx - cos3x/cosx = 2

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Q: 3) (sinx + cos x)² = sin 2x + 1 COS %3D

A: We have to prove that  (Sinx+cosx)^2=sin(2x)+1

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

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

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

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Q: Integrate e^(2theta)*sin(3theta)

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Q: Evaluate V2 cos sin-! 2.

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Q: Express the product sin 4x cos x as a sum or difference.

A: Given: sin4xcosx

Q: Express as a sum or difference.3 cos x sin 2x

A: To express: The expression 3cos x·sin 2x as a sum or difference. Given: The expression is 3cos x·sin…

Q: (ii)V 1 – sinx (in) 1+ cosx 1 + sinx sinx

A: i)Given, 1-sinx1+sinx Take conjugate of denominator term and multiply it with both numerator and…

Q: sin(13z) sin(9z) dz

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

Q: 9. Use the Residues Theorem to calculate 1+ sin² ª -de. Sketch the contour you used.

A: We have to find integral using Residue Theorem.

Q: Prove Sine tan 2. 1+ cose

A: Using the double angle identities we get

Q: tan e de sece+ 4 cos € COS

A: The given integral is tan(phi)/[sec(phi)+4cos(phi)]

Q: Verify the identity by transforming the lefthand side into the right-hand side.

A:

Q: sec(x)cos(3x)=0 from [-pi/2, pi,2]

A: sec x cos 3x=0          [-π/2,π/2] sec x (4 cos3x - 3 cos x) = 0 [cos 3x= 4 cos3x - 3 cos x] 4 sec x…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.