3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show these estimates are the best possible, by giving values of a and b for which the bounds are actually attained.

Q: (). 11T 12 a) Using a sum or difference formula,find the exact value of sin cos(a + B) = 1- tana tan…

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Q: 5. Which of the following has the largest value? A. sin 2 B. sin 2 C. cos 2 D. cos' 1

A: A. Let sin-112=x. 12=sinx12=sin30° B. Let sin-132=x sin-132=x32=sinx32=sin60°.

Q: If Cos √3 2 calculate the value of O = and tan 0 = . where 00 < 2TT.

A: we are given the values of two trigonometric functions, we need to find out the value of the angle…

Q: Let P be an approximation of pai accurate to n decimals. Show that P + sin P gives an approximation…

A: Substitute the value of P in |f(x)|.

Q: (b) Compute sin 20. Hint: sin 20 = sin(e + 0)

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Q: LET COS (2B) = 1. COMPUTE THE VALUES OF B, ON [ 0, 2 * PI]

A: We have given equation  cos2B=1 cos2B=cos0=cos2π=cos4π 2B=0,2π,4π B=0,π,2π

Q: V5 , where 0 < x < . Find the exact value of cos Suppose sin x = (즐). 3

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Q: (a) Show that cos(x²) > cos x for 0 ;. 1

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Q: 10. Show that there is a root of cos(x): = in the interval (0,7). TT Do NOT find the root. Explain…

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Q: Find all solutions to the following equation on the interval [0, 27]. .cOS X

A: Here, we need to find the solutions to πcosx=π. So,…

Q: Express the number 2/3 – 8i in the form R(cos(0)+ i sin(0)) = Reo, where R> 0 and -T <0 <T. NOTE:…

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Q: 9.[4 pts] Suppose that - 1<x< 1. Circle all the correct statements: sin-¹ x must be positive cos¹ x…

A: Solution- if value of X lies between -1 to +1   let X =12⇒0.5,X=0.80    We will check the given…

Q: (2) Prove that for any integer L () NTX / sin? dx = L. L -L

A: ∫ cos(ax) dx = 1a sin(ax) +C