Solve the equa tion on the interval [ o, 2 ) 2 sin? 9-3 sin O +1 =0 tan2x-1 =0 (2 cos x +JE) (2 sin x +1) = 0 2 cos?x + sin x-1 =D0 X + sin x-1 =0

Q: 20 a Show that sin (A + B) + sin (A – B) = 2 sin A cos B. b Hence find: i 2 sin 3x cos 2x dx ii sin…

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Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

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: 5. Given that 2 sin 20 = cos 20, a) show that tan 20 = 0.5. b) hence find the values of 0, to one…

A: given that 2sin2θ=cos2θ to prove that tan2θ=0.5 proceed as follows  2sin2θcos2θ=1tan2θ=12tan2θ=0.5

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: Value of L is 16 $3+9s 16 O(1 + sin 31) 16 O (1 + cos 3t) 16 (1+ cos 3t) 3 (1 - cos 3t)

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Q: Q3-Prove that (cos303cos³ 0-3cos 0 sin? 0)

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Q: 2. : (a) For n ≥ 1, show that 1+z+2²+...+ 2¹: (b) Hence, show that 1+ cos 0 + cos 20 + 12+1 2 #1 7…

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Q: 6) What is the period of the function f(x) = 7sin(2x) – cos(5)? Is the function g(x) = 7xsin(2x) –…

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Q: iii) E(-1)"+1 cos²(÷) COS n=1

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Q: 3. Show that the equation 1 + cos(x) – 2sin(=) = 0 has a solution in the interval [0, 7 /2].

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Q: Using appropriate substitution, sin³ (3x)cos*(3x)dx is equal to -cos"(3x) + cos"(3x) + c - cos (3x)…

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Q: Q.3- Prove that: 2n 1 (cos =0 +i sin-) + 10 2cosne eino

A: The given problem is to prove the following complex identity. (cos n/5 θ +i sin 2n/10 θ)+1/einθ =…

Q: Assuming In = [ cos" xdx. and n > 2: 1 п -1 n-1 r sin x + -In-2; CoS' In n %3D n

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Q: 10. Prove that 7/2 sin 0 cos ! (cos a cosec 0) d0 /2- TC (1-cos a). COS

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Q: 4. (a) Express 3cos x-4 sin x in the form R cos(x+ a) where R>0 and 0 <a < (b) Hence find the…

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Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

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Q: the integral F(®) = cos*(0) + sin(20) – 3 cos(0) COS do sin (0) +3 cos2(0) + 2 sin(0) – 3

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Q: In Problems 28–44, establish each identity.

A: Trigonometric identities are given, we have to prove the identities. Note: we are answered with 3…

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: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: Q1: (1) Show that the value of € (-1, π), for which: sin² 0 1+ sin² 0 sin²0 1 + cos²0 cos² 0 cos²0 4…

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Q: Find the exact values of sin and cos for sin e= on the interval 0° s es 90°. 2 sin 0.1691, cos…

A: We know that,  cosθ=1-sin2θ         cosθ&gt;0 in 0°≤θ≤90°        ⋯⋯1sinθ2=1-cosθ2…

Q: Hi, there are two questions a) and b) attached  Thanks so Much!!!!

A: (a)consider the given complex number:

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: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9x)-cos(4x) +c Select one: True O False

A: topic- indefinite integral

Q: 8. Find all 0 such that -180° <0 < 180° and: cos 0 = - b sin 0 = c tan0 = - a d cos 0 = 0.8 e tan 0…

A: we have given -1800≤θ≤1800a. cosθ=-110⇒θ=cos-1(-110)=95.740b. sinθ=45⇒θ=sin-1(45)=53.130c.…

Q: (-1)"x2" Σ (2n)! 1. For all x E R, cos x = n=0 +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b)…

A: We have to prove the sum of series.

Q: 9-10.j Show that sin20 2tane %3D 1+tan20

A: We will prove the trigonometric formula.

Q: II Find sin .2 4), and tan4) from the given in 2. 10 sec(x) = , 270° < x < 360° %3D sin 2 (즐) - %3D…

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Q: 10. Prove that 7/2 TC sin 0 cos (cos a cosec 0) de /2-a (1-cos a). COS

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

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Q: VERIFY THE IDENTITIES

A: To verify

Q: - Prove that tan 0 + cos 0 sin 0 cos 0 cos 0T sin 0 - Prove that cos? 0 – sin² 0 cos? 0 + sin A cos…

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Q: 10. Prove that 7/2 TC/2- sin 0 cos (cos a cosec 8) de -0 2 (1-cos a).

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Q: 1. Express as a sum or difference a.) sin 7t sin t b.) cos 6u cos (-4u) c.) cos 2t sin 6t d.) 2…

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Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

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

A: Using compound angle formula &amp; trigonometric identities.

Q: 0.3- Prove that: n 2n 1 (cos =0 +i sin8) + 10 2cosne - 5 eine

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Q: 4 sin 2t + 2 tan 2t = 0 %3D

A: 4sin2t+2tan2t=0

Q: 7π/4 Evaluate the integral (sin x+ cos x) dx using the fundamental theorem of calculus. Discuss 2+…

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Q: 1 In 3n 1 sin (3x) [cos"-1 (3r) sin (3r) + 3(n – 1)In-2] %3D I1 = %3D - 3 What is I, ?

A: Given : In = (1/3n)  [cosn-1 (3x) sin (3x) + 3(n − 1)In-2 ]  I₁ =  (1/3n)sin (3x)

Q: 1) Use De Moivre's theorem to show that cos 50 = cos' 0-10 cos' 0 sin20+5 cos 0 sin* 0 and sin 50 =…

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Q: 5) Determine the following indefinite integral cos (3x) (1 – sin(3x))(2 – sin(3x)) -dx

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Q: 2- Exercise: Evaluate a) L{4x? – 3 cos(2x) +5e*} b) L{4+sin (x) – e**}

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Q: 1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps that: cos? x = %3D…

A: Note - Since you have posted multiple questions, I am answering first one for you as per the…

Q: de 2- sin(e) ( cos(e) de 1+cos(0) de 2- 3sin(e) de 3sin(e) + 4cos(e) + 5 de sin(e) + 3cos(6) + 3

A: SOLUTION Given ∫dθ2 -sinθ∫cosθ dθ1+cosθ∫dθ2-3sinθ∫d θ3 sinθ+4 cosθ+5∫d θsinθ +3 cosθ+3 we need to…

Q: 2. Prove the reduction formula: (5 pts) n-1 sin x cos n - n-2 | cos" xdx = cos" xdx

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