Prove the following. Provide all necessary solutions. 1.) [sin^2/cos] + [(csc*sin)/sec] = sin (tan + cot) 2.) [1/(sin*cos)] = tan + cot

Q: 2: Prove that a) cosx tan3x = sinx tan’x b) (sin x + cos x)² = 1 + sin 2x

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Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

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Q: Verify the identity : 1-cosx sinx = 2 csc x sinx 1– COsx 2.

A: Given- 1-cosxsinx+sinx1-cosx=2cscx To verify- The above identity. Identity Used- sin2x=1-cos2x

Q: State the half-angle identities used to integrate sin2 x and cos2 x.

A: Given, The functions are sin2 x and cos2 x

Q: QUADRATIC TYPE 6) sin 0 + 1- cos 0

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Q: Solve the equation 2sin2 x + cos x = 1 on the interval [0, 2π). Use exact values where possible or…

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Q: Solve the equation sin 2x + cos x = 0 on the interval [0, 2π). Use exact values where possible or…

A: Given

Q: Find SinZx, Lo52x, Tan2x Cosxニーニ 3. and X terminates in quadrant 2 Sin2x = Cos 2x = tan 2x =

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Q: verify that cos(alpha-beta)/sin of alpha sin of beta is = cot of alpha cot of beta +1  please show…

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Q: solve the equation on the interval [0,2π)  cosx+2cosx sinx=0

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Q: 5)Prove that (1+sinx)(1+sin(-x)) = cos²x (manipulate left side in order to get right side) %3D

A: We have to prove the given identity: 1+sin x1+sin -x=cos2 x We know that sin -x=-sin…

Q: Solve in interval [0°,360°). sin² 10z + cos² 10z = 6 cos z 80.41, 260.41 80.41, 440.41 80.41 ,…

A: It is known that sin2θ+cos2θ=1 for all θ.   Use the above known fact in the given equation and…

Q: tan(2x) O 1+ cos(4x) sin(4x) O cos(4x) – 1 sin(4x) O 1- cos(2x) sin(2a) sin(4x) 1+ cos(4x)

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: cos 2x= 2- cos 2x

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Q: Prove sin 2x cot x (1 - cos 2x)

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Q: Approximate all solutions to 8.cos(x)2 –6.cos(x)+1 in the interval [0°,360°) X= degrees Round your…

A: The given equation is quadratic in cosx.

Q: Find all solutions of the given equations in interval [0,2π) tan(x/2)=sinx

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Q: Prove the equation Sin^2xcos^3x=(sin^2x-sin^4x)(cosx)

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Q: tan(2x) = O cos(4x) – 1 sin(4x) COS O 1+ cos(4) sin(4x) O 1- cos(2) sin(2x) sin(4x) 1+ cos(4x)

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Q: Find all solutions of 4sin^2xtanx−tanx= 0 that are in the interval [0,2π)

A: Given the equation  4sin2xtanx-tanx=0. We need to find the solution in the interval [0,2π)

Q: Find the possible values of x in |coshx -sinhx| = 2 Isinhx coshx

A: Given,           coshx-sinhxsinhxcoshx=2

Q: Prove Cos (3x)- cos (7x)/sin (3x+sin (7x) =tan (2x)

A: To Prove: Cos3x-Cos7xSin3x+Sin7x=tan2x Formulae to be used:…

Q: Compute sec() if sin(0) = 0.29 and 0 < 0 < 5 Give you answer accurate to 4 decimal places

A: Find your answer below

Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: Verify the identity: 4 cos x cos 2x sin 3x = sin 2x + sin 4x + sin 6x

A: We have to verify the identity: 4cosxcos2xcos3x=sin2x+sin4x+sin6x We know that…

Q: How many solutions on the interval [0, 2020π] does the equation 1/2 sin2x + 1 = sinx + cosx have?

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Q: Prove that the equation sinx = 0.3 has at least one solution in the interval(o, π/2).

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Q: Verify the identity. cos 7x- cos 9x tan 8x sin 7x- sin 9x Statomont

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Q: Determine two smallest roots of the equation x.Sinx + Cosx = 0 using Regula-falsi method, correct…

A: Consider the provided question,  xsinx+cosx=0Let fx= xsinx+cosx here, x 0 1 2 3 f(x) 1 1.3818…

Q: prove that = - Cotx + C 1- cosx +Sin'x

A: According to the question, we need to evaluate the integration: F(x) = 2(1 - cos2x + sin2x) We need…

Q: Prove that sin3x/sinx - cos3x/cosx = 2

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Q: Prove 2tan x cos (3x) = sec x (sin(4x) - sin (2x))

A: Topic- trigonometry

Q: prove that: sin7x.cos3x-cos7x.sin3x/tan2x=cos4x+1

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Q: 1) Solve (tan(x)−1) (3tan(x)+√3) over [0,2π) 2) solve sin2(x) − sin(x) = 0 over [0,2π

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Q: How many distinct solutions does the equation 2 sin 2x = - -V3 have in the range [ 0°, 360° )? Enter…

A: To find the distinct number of solution does the equation 2 sin2x=-3;    x∈[0°, 360°)

Q: prove that catX+c - Cos'x+Sin2X

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Q: If cos(x)=sin(x)=0.5 , find the following:   1) (sec(x))^3 2) sin(2x)+(cos(x))^2 3)…

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Q: Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13 %3D

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Q: Prove (secx+tanx)/(secx-tanx) = (1+2sinx+sin^2x)/cos^2x

A: To prove that   (secx+tanx)/(secx-tanx) =(1+2sinx+sin2x)/cos2x

Q: prove that cos^2 x/2= tanx+sinx/ 2tan x

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Q: Solve the equation on the interval [0,2π). (tanx+1)(cosx+1)=0

A: The given equation is

Q: Find the indicated number (i) sec-(-2v3/3) (ii) cos(sin-12+ sec-1 3)

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Q: prove the identity sin^2xcos^2x+cos^(4)x=(1-sinx)(1+sinx)

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Q: Solve for [0, 2T1]. -Cos (7x) + cos x = -Sin(3x) COs + coS x -sir

A: Given equation is By using the formula we get

Q: compute:   ∫sin^3xcos^2xdx

A: We have to find:

Q: Prove CotA= sin2A/1-cos2A

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Q: Prove (sin10x)/(sin9x+sinx) = (cos5x)/(cos4x

A: Explanation of the prove is given below..

Q: Approximate all solutions to 8-cos(x)² – 6·cos(x)+1 in the interval [0°,360°) x = V degrees Round…

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Q: Verify that 2tan (x/2)= (sin2x+1-cos2)/(sin x(1+cos x)

A: Consider the given condition that,2tan (x/2) = (sin2x+1–cos2x)/(sin x(1+cos x)) … (1)Consider the…