Prove the following identities. 4. cos3a = 4 cos' a – 3cosa

Q: Integrate the following with respect to t 20 cos30

A: Solution:To integratelet I=∫2θ cos3θ dθFormula:∫ cos aθ dθ=sin aθa+C ∫ sin θ dθ=-cos…

Q: b)Estimate the value of cos 0, at 0 = 5°with the help of the following table 0: 0° 10° 200 30° 40°…

A: If θ be an angle in a right-angled triangle, then the sine of the angle or sinθ is defined as the…

Q: b)Estimate the value of cos 0, at 0 = 5°with the help of the following table 0⁰ 10⁰ 20⁰ 30⁰ 40⁰ 50⁰…

A: The given table is: θ 0 10 20 30 40 50 sinθ 0 0.1736 0.342 0.5 0.6428 0.766 We have to…

Q: Given the ODE (cscy)dx + (cos²x)dy = 0. A one-parameter solution of it is: O cosy + tanx = c siny =…

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Q: Verify the identity: cos A sin' A 1 %3D 1 – cos A -

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Q: Verify that the following equation is an identity. cos 2x + cos 2y = 2 cos x + 2 sin y cos x- sin y

A: We use the following identities cos(2x)=2cos2x-1sin(2x) =1-2sin2x(a2-b2)=(a+b)(a-b)

Q: 4.) Prove the identity. csc e Csc 20 2 cos e

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Q: Prove the following identities. a) cos (37 + x) x = sin x 2

A: Follow the procedure given below.

Q: Let csc t = radical 37  with t in QII and find the following. cos 2t

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Q: Find 0, if 0° <0 < 360° and 1 and 0 in III. 2 cos 0 =

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Q: If 0 = then 3 %3D sin(8) = %3D cos(e) = %3D

A: We have  this can be also written as

Q: B Integrate the following. * cos x' dx 2 a.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Show that the following is true. cos(180° - 0) = -cos e

A: You know the formula:

Q: 10. Compute the following: »TT/4 (a) COS dx 3 (b) dax

A: Part (a)-Given:

Q: Q2/provethate Cos17 +SinI7 cos17-Sın17 %3Dtun62

A: We have to prove that                               cos17°+sin17°cos17°-sin17°=tan62°

Q: Show that 0 π/2 st sin? xdx TT/2 [ 0 cos? rdr 2

A: A detailed solution is given below.

Q: TT TT Solve the following: cos (x +-) – cos(x – –) = 1 for 0 < x < 2n.

A: Given that: cos(x+π6)-cos(x-π6)=1                         0≤x≤2π

Q: Prove: L{cos at} = s2+ a?

A: We will prove the given statement.

Q: 2² cos(x³ – 1) dx .3

A:

Q: 4. Evaluate the following and give the exact value: - Tt/4 r2 cos 0 crsin 0 r2 cos 0 dz dr d0 0,

A:

Q: Find the exact value of cos 5p 12

A: We have to find exact value of the trigonometric expression: cos 5π12 Rewriting the given…

Q: If 0 = then 6. sin(0) = %3D cos (e) = %3D

A: Given θ=5π6. We know that sinπ-α=sinα and cosπ-α=-cosα

Q: Evaluate. S cos a In(secz)dr COS D

A:

Q: COS xdx

A:

Q: Prove the following identities and give the val- ues of x for which they are true. cos 12 sin-lx2 =…

A: cos2sin-1x Now let, sin-1x=θ Therefore, cos2sin-1x=cos2θ=1-2sin2θ      ∵cos2x=1-2sin2x=1-2x2…

Q: Let sin A = - with 270° SAS360 and cos B% = 24 25 sin(A + B) 4/5

A: The given values are Now, to find the value of sin(A+B), use formula

Q: 1. Evaluate the following using (a) (2² – x) cos r dz

A: (a)  Given: ∫x2-xcosxdx

Q: Compute the following. S3x?cos(x³)dx

A:

Q: 2-Find O for: y3tan? (cos x).

A: Using Chain rule we can solve the given derivative problem

Q: .Inside the outer loop of the limason r 1-2 cos e

A: Given that r=1-2cos(theta) We have to find area.

Q: Verify that the following equation is an identity. cos 2x + cos 2y =2 cos x + 2 sin y sin y COS X-

A: We can use basic trigonometric formule to prove the Identity

Q: find the exact value cos151ocos1o + sin151osin1o

A: We have to use cosAcosB+sinAsinB= cos(A-B)With A=151 and B=1

Q: 5 1. If sec a with a in quadrant Il and cos B = with B in quadrant IV evaluate: 3 a) sin(a- B) b)…

A: If sec α=-52 with α in quadrant II and cos β=13 with β in quadrant IV, then to evaluate the…

Q: At what value(s) of x does cos x = -x?

A: Given,

Q: Show that the following equation [ has a solution on (0, 2). 42-1 = πX 2 5 cos(-

A: The given equation,       4x-1=5cosπx2

Q: E. Prove. 1+ cos20 – cos²0 = cos20 %3D

A: To prove:- 1+cos(2θ)-cos2(θ)=cos2(θ)

Q: 1. If 0° < 0 < 90° and cos 0 = , find cos O V42 O √42 O V 047

A: Topic = Trigonometry

Q: Q2\ Prove the following identities sin 20+cos 20+1 a) = cote sin 20-cos 20+1

A: Here given equation   sin 2θ+cos 2θ+1sin 2θ-cos 2θ+1=cot θ

Q: D. Express each of the following as a product of circular functions. 1.- sin(-20) + 3sin20 2. cos 3x…

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Q: d) Verify the following identity cos 0 + sin e = 2secs e 1+ sin 0 cos 0

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Q: Find the smallest number x such that cos(e^x + 1) = 0

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Q: 20 Establish the identity: 1- cos e sin e sin e 1 + cos e LHS Sunt

A: Let us prove the given identity.

Q: Let sin A = with A in QII and cos B = - with B in QIII. Find cos(A+ B) %3D

A: Given :

Q: 1 La So cos " dy dæ COS evaluate

A: We are given the Integral: ∫π2π∫0x21xcosyxdy dx=∫π2π1xsinyx×1x0x2 dx=∫π2π1x2sin xdx It cannot be…

Q: 1 (a) Calculate and fully simplify |a² cos(z) dz.

A:

Q: At what value(s) of x does cos x = 9x? X=

A: Cos x= 9x To find the value of x

Q: Integrate the followings sin cos dx cos - 4

A:

Q: 3. Verify each of the following identities. cos? 0 a. sin 0=1-- 1+sin e

A: