VII. Verify the identity. 11.) sin 3x = 3 sin x-4 sin3 x

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

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

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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: (c) Prove that sin x 7C sin 2 x2 dx +4x+5

A: The integral function is ∫-∞∞sinxx2+4x+5dx

Q: 2+7 sin z 3. dz cos? z

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3- Represent in the form of x+ iy a) V8 (cos + i sin m) b) 6 (cos 7 + i sin7)

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Q: 6. Prove the following sin (x + n) = -sin x cos x+ 2 - sin x

A: Part a,Given,           sinx+π=-sinx

Q: 5. Verify the identity: sin(x- y)cos y+cos(x– y)sin y = sin x

A: Explanation of the solution is given below.....

Q: 4. Verify the identity sin(z+y) %3D COB E COS y tan z+ tan y

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: S Show that L(cos² 3t – sin² 3t)= 82+36

A: Using Laplace transform,

Q: 57 where 2 tan 0 = <0 < 3T 3 Find sin 20 7 24 24 25 24 25 25 24 4,

A: By using sin(2x) formula in terms of tan(x).

Q: S 3. sin°ydy 1+ cosy

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Q: 7 with A in QIII and find the following. 25 Let sin A = - sin 2A

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Q: 2). Express the following : > 20° in radians. T/9 rad in degree. 2b). prove that: (sinø-cosø)^2 +…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Evaluate So sin(x) dx 1+sin(x) 2 Select one: O 1+ 2 2 -1-5 -1+5 2 2

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Q: 20. What is sin 17t? а. 1 b. -1 С. О d. undefined

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Q: 1) Find thesexact value o niSinG/2) ban sin x Ei Joven that 4 2.

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Q: 9. Evaluate. Give the exact answer, not a rounded off decimal. a. tan−1 (√3) b. sec (sin−1 ( 5 13))

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Q: Show that (1 – e") = 2 sin ( - a eil(a-r)/2]

A: To show 1-ejα=2 sinα2ejα-π2 , simplify left hand side expression and show equivalent to right hand…

Q: Rewrite 1 sin(x)+ 2 cos(x) as A sin(x + 4) %3D Note: o should be in the interval-T <¢ < II

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Q: 40 a) Find sin' xcos' xdx by using substitution u = cosx.

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Q: 1 what is sin(-x)? 7 Given that sin(x) =

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Q: 4. If x= sin² and y = 1 when x = 0, then find the value of x when y = 3. 0 O 8 None of these

A: Topic- differential equation

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: 19. Solve for x:x = (tan e + cote)² sin?e - tan?

A: Given that: x=(tanθ+cotθ)2sin2θ-tan2θ

Q: 3 3. Find the value of cos(2x) given that sin x = -and x is in QII.

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

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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: 1 ,3 -r/a0 ? 0 ,² dr sin0d0 ø do = x 32na cos X = ? 0 Jo Jo

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Q: tan? 20° – sin? 20° Compute: Show your work. tan² 20° sin² 20°

A: Given  tan220°-sin220°tan220°sin220°

Q: 3. What is (Sin (6x)}? 4. What is (Cos (x²) dv 5. What is (tan x³) dx 6. What is (In x)7

A: we use the chain rule to find the derivative of the given function

Q: ( esch(3 tan z) + sin². 1. cos? r

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Q: 3. Express into standard form: = = 8[cos (-5) + + sin(-5)] Z i 3 3

A: Solution

Q: 4. Verify the following identities: a. sin 3x = 3 sin x-4 sin3 x b. 1+ cos 10x = 2 cos? 5x %3D

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Q: 14. An expression that is equivalent to sin 2x is 1- cos 2r tan r

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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: 17) Prove the following: a) (sin x)(sec x)(cot x) 1

A: Since secx=1cosx  and cotx=cosxsinx Then LHS =  sinxsecxcotx=sinx1cosxcosxsinx

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

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

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Q: *7/2 Evaluate sin" x cos x dx for n > 0.

A: ∫0π2sinnxcosxdx Substitute t=sinx Differentiate the above equation dtdx=cosxdt=cosxdx Upper limit at…

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

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

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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: 1 Q:Evaluate: 3 sin x+cosx

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Q: 3. If tan(a-iß) = x- iy , show that x? + y?-2ycoth2B = -1

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Q: S(x) - e 05 (2 cos 2.x+3sin 2.x) 7. , evaluated at x 1 rad

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Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

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