b) Explain how you would find sin" x cos" x dx if i) m is odd and positive, n is odd and positive, iii) ii) m and n are both nonnegative and even.

Q: → find period of 8- @yotan 2 y. 5 cos 1o* 10 yo 11

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Q: Express in the form a + bi where a and b are real numbers.

A: Here given equation is cos 2π/3 + i sin 2π/3 = cos 60° + i sin 60° = 1/2 + i 3/2

Q: 1 (5) 1- cose 1+cos 0 sin?0

A:

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: Q5. If coshx = csc20, prove that 0 = n+ cothe¯. [Hint: use identity sin(2a + 2n)] %3D

A: given that                                                                             coshx=csc2θ…

Q: 2) If y = cos x, what is y (®(x)?

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Q: Assume that sin u = 3/5 and sin v = 4/5. Find cos (u - v). I need all work.

A: Given:

Q: 7. Let tan u = and sin v = , with n <u < and < v<T. Find the exact value of sin(u – v). 13

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Q: Prove that: 1-tan? 0 cos? 0 - sin? e %3D 1+tan? 0

A: A function is said to be a rational function if it is given as the ratio of some values.  The…

Q: sin (+) can be expanded to: π TT O sin COS sin sin 4 7 TT O sin sin COS cos 4 T Osin COS + cos sin…

A: Solved below.

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: B. If sin u = tan u < 0, find : 1. sin u/2 2. cos u/2 3. tan u/2

A: Given that, sinu=tanu&lt;0

Q: 1. Explain why sin(n+0) =-sin@ using a diagram and x, y, and r.

A: Solution of given problem is followed by

Q: 2. To create an identity for the equation cos x( 1+cotx) = A, where A would need to be A. cos'x B.…

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

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Q: 1- cos4x sin?xcos?x %3D 8

A: some formulas: 2sinxcosx=sin2x1-2sin2x=cos2x2cos2x-1=cos2x Given expression is: sin2xcos2x Multiply…

Q: 3. Are reduction formulas needed to evaluate sin x cos? x dx? Why or why not?

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

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Q: 2) Verify that the equation is an Identity. tan 0 = sin 0 %3D sec 0

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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: If ex = tan 0, then sin e: O 1 - cos e 1 ex

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Q: Another form of sec x dx cos x 1- sin²x b. Use the identity in part (a) to verify that 1. |1 + sin…

A: a) we have to verify the identity sec(x)=cos(x)1-sin2(x)Consider, RHS=cos(x)1-sin2(x)we…

Q: 15. Restate r= 5 cos 0 in rectangular form.

A:

Q: . Suppose csc(A)· where A terminates in QIV, and sec(B) = -3 where B terminates in QII %3D a) First…

A: Note the trigonometric identities :

Q: Part 3 of 4 COS X d —CSC X + С dx To check for the result, prove that 1 - cos?x

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Q: fiken tan o = ý and sin o ro al CoS e b) CSc e 4)

A: Explained below

Q: B) Prove that: cos? 0 – sin? 0 1-tan? 0 =- 1+tan? 0

A: B)cos2θ-sin2θ=1-tan2θ1+tan2θRHS1-tan2θ1+tan2θ

Q: 2) Verify that the equation is an Identity tan 0 %3D sin 0 sec 0 %3D %3D

A: We know that secx is the inverse of cosx and tanx=sinxcosx the objective is to prove the…

Q: Show that the equation sin(cos 2x)= V1-4x² is an identity. %3D

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Q: To evaluate tan z cos z dz, we may substitute u= cos z.

A: Given,          ∫tan3xcos2xdx

Q: 2) Verify. cot8 ese 6 %3D sin 6 tan 6

A: Use the following identities:

Q: 1 In right triangle ABC, mZA = 30° and mZB = 90°. Which of the following are true? I. sin(A) =…

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Q: The smallest positive number for which sin(2x) – sin z = 0 is z = %3D Hint: Apply a multiple angle…

A: We have to solve the trigonometric equation: sin2x-sinx=0 We know that sin2x=2sinx cosx So,…

Q: ngle Belo 1. Sin B = 30 34 2. Cos B = 3. Tan B %3D 16

A: Given problem:-

Q: If cos(x)=A, cos(y)=B, sin(x)=C and sin(y)=D, find an expression for sin(2x+y) which only involves…

A: If cos(x)=A, cos(y)=B, sin(x)=C and sin(y)=D, find an expression for sin(2x+y) which only involves…

Q: The integartion of [sin(sinØ)]Ø cos dø Is: cos(sin0)+C -sin(cos Ø) + C O -sin(sinØ) + C O -cos(sinØ)…

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Q: ( esch(3 tan z) + sin². 1. cos? r

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Q: 2 Convert r = to rectangular form. 7 sin 0 COS

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Q: Express as a sum or difference:4 sin 3 θ cos 7 θ

A: Consider the provided expression, 4sin3θcos7θ Express as a sum or difference. Use the formula of…

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: Show that sin x – cos x< V2 V2 -

A: Take RHS first and work on that:

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: If z = os0+ I sin 0 and y= cos Isin p, then show that %3D 2 cos(@-).

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Q: v in the quadrant IV COS (U+V)=

A: we have to find the exact value of cos(u + v) given that sin u=-3/5 with u in quadrant III, and sin…

Q: sin(x + y) – sin(x – y) = 2 cos x sin y

A: sinx+y-sinx-y=sinx cosy+cosx siny-sinx cosy-cosx siny=sinx cosy+cosx siny-sinx cosy+cosx siny=cosx…

Q: (3) Prove that Sina cos a -Sinß cos B sin cos B sinß cosy sin(2+ B+y)

A: We have have to solve given problem:

Q: Prove by MSE that a. sin 90° = 1 b. cos 180° = -1

A: