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

Q: sin 0 + In + 22+3 = -3 - cos 20 - In y? + 327-4 = + 2ln y+ 22 -3 1+ (cot 0)2

A: Given system is sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: Hiw ABy using Euler's formula prove That : sin(-2)= cosz

A: Euler's formula  Sun(a-b) = sinacosb - cosa sinb

Q: 47' sin z = x³ . cos z + sin z - 3z² Select one: True False

A: Given that d(x3 sinx)/dx  . Here we derivative of this question with respect to x. We know that…

Q: 3. Express 1+cos2x in terms of cos x. hence a. Evaluate (1 + cosx)dx b. Express 1- cos2x in terms of…

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Q: s nip

A: Given z=tanα2

Q: 04) Prove that 1- Cos + x) = sin x, 2- (sin x +cos x) sec x = sec2 x %3D

A: We have to prove that following trigonometric identity.

Q: 1-sinx cosx 2. a) Show 6) Prove 3sino – 4sin0 = sin(30) cosx 1+sinx

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Q: Q3. Use substitution to show that x = n is a solution to the equation sin(x) – cos(x) = 1. Show your…

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Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: 3. Prove that the identity is true. sin*t- cost = tan²t-1 cos't

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Q: EX-15- Prove that : a) Sec-'x= Cos- ! b) Sin-' (-x)=-Sin-'x

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Q: Find all values of x in the interval (0, 27] that satisfy the equation sec2 x + 2 cos² x = 3

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

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Q: cos" xdx :0. 6. If n is a positive odd integer, prove that

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Q: 1) Prove that sin 0 tan 0 + cos 0 = sec 0.

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Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: 1. If z = sin2+In^, find the value of x- +y X

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Q: (2k + 1). True or False tan 0. cos 0 = sin 0 for any 0 + %3D

A: Given :            tan θ . cos θ = sin θ for any θ ≠ (2k + 1)π2.  To state true or fase.

Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: Q4: Prove that: cos?x – sin?x cos²x - 1- tan?x

A: We need to prove that cos2x-sin2xcos2x=1-tan2x We will use tanx =sin xcos x

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

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Q: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

Q: Prove: sin? x 2 cos“ = cos 2-2cos x

A: We will use basic properties of trigonometric ratios

Q: The solution to the equation sin 2x =-sin(-x) in the interval (0, 2z) includes 0, n A. B. ,0, z 3 3…

A: We can solve the question as per the criteria and conditions given.   NOTE :: As per our guidelines…

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

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Q: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

A: The given expression,      cos 2θ-isin 2θ8cos 3θ+isin 3θ2cos 4θ+isin 4θ3cos 2θ-isin 2θ5 De Moivre's…

Q: 4.) Prove: sin 2x a) 2cos? x = tan x b) sin 3x = 3 sin x – 4sin3 x [Hint: sin 3x = sin(2x + x)] -

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

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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: Prove the identity. s (xxy) sinx- sin (x-y) cosx= siny cos

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Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same time) 1.…

A: sin2x=1-cos2x and,  tanx= sin(x)/cos(x)

Q: Q4) Prove that 1- Cos +x) = sin x, 2- (sin x +cos x) sec x see' x

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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: VERIFY THE IDENTITIES

A: To verify

Q: Can the Intermediate Value Theorem be used to prove that the equation 9 2(r + 9) sin*(x) – 4 cos"(x)…

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Q: e). Prove that Sin3A+sinA 25in2A -COSA

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Q: Q3-Prove that (cos30=cos³ 0-3cos 0 sin? 0)

A: Using compound angle formula & trigonometric identities.

Q: sin 2x sin x Cos 2x %3D Prove that 4 cos x - sec x Cos a

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Q: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

Q: USE THE SECANT METHOD IN FINDING ROOT/S STARTING AT XI-1=-0.1 AND XI=0. (NOTE: UTILIZE UP TO 4…

A: Given : fx= cos x +2 sin x +x2      xi-1=-0.1   and  xi= 0 To Find : Root of  equation by secant…

Q: 1) Use the false position method to find a root of the equation x³ = -cos x in the interval [-1, 1]…

A: To find a root of the equation x3=-cosx in the interval -1,1 with εs=0.0005% Let us consider the…

Q: 23, sin 50° + sin 40° 23. sin A VZ cos 5° B 2 cos 10° 2 cos 5° D V2 cos 10°

A: Trigonometric identity: sin x+sin y=2sinx+y2cosx-y2

Q: tx)+ Sin(꼴-)- -26S X %3D Prove sin

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Q: Show that : |sin x |= CoS nX Σ n2 even 414 2/7

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Q: prove it 6. *cos 4x = 1 - 8 sin?x + 8 sintx

A: Prove : cos 4x = 1 - 8 sin2x + 8 sin4x