Verify the identity. csc(x) cos²(x) + sin(x) = csc(x)

Q: Question in Image.

A: To Determine: Find the exact value :

Q: Express cos- (a) in terms of cos(2a). Express sin (a) in terms of cos(2a).

A: This question is of double angled identity.

Q: 2 -3 sin x 2. Find + 4e*+3 dx. cos? x

A:

Q: Locate and identify the absolute extreme values of a. ln (cos x) on [-pai/4, pai/3], b. cos (ln x)…

A: a.Given:

Q: Prove the identity. +x + sin 6. sin = cos x

A: Given, We have to prove the identity sinπ6+x+sinπ6-x=cosx

Q: Find the exact value of cos2 15° - sin2 15°.

A: We have to find the exact value of cos2 15°-sin2 15°Formula used :-Cos 2θ= cos2 θ-sin2θ -1

Q: 3 sin° x -dx Evaluate ' cos° x

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Q: (÷++) + co« (5 - ). cos 3 x ) is equivalent to O cos 2x cos x O sin x cos x

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Q: Prove the identity. Cos(x− 90°) − Cos( x + 90°) = 2 sin x

A: We will use the formulas: cos(A-B)=cosAcosB+sinAsinBcos(A+B)=cosAcosB-sinAsinB

Q: Verify the identity: sin4 t - cos4 t = 1 - 2 cos2 t

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Q: Prove the identity: cos(x + y)cos(x – y) = cos?x – sin²y

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Q: Using (11) and (12): 1 dx 1+ cos x tan +c

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Q: What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x +…

A:

Q: Prove the identity (sin x + cos x)? – sin(2x) =1

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Q: Locate and identify the absolute extreme values of cos (ln x) on [1/ 2, 2].

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Q: Prove the identity step by step.  cos4 x-sin4 x=cos2x

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Q: -5 sin x = -2 cos2 x + 4

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Q: Dhcx)=cos (x+)

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Q: Verify the identity sin 4t = 4 sin t cos3 t - 4 sin3 t cos t.

A: We have to verify the identity: sin4t=4sintcos3t-4sin3tcost We know following trigonometric…

Q: 3 3. Find the value of cos(2x) given that sin x = -and x is in QII.

A:

Q: Verify the identity. cos² t sin t -=cos tcot t

A: We have to Verify the given  identity cos2tsint=cost cott

Q: cos 2r Verify the identity: = cos x + sin x. sin x cos X

A: Verify the following: cos 2xcos x-sin x=cos x+sin x

Q: Use an identity to solve the equation cos 2x = cos x on the interval [0, 2π).

A: Given:cos2x=cosx on the interval [0,2π)Formula:cos2x=cos2x-sin2xsin2x=1-cos2x

Q: prove the identity  sin(x) + sin(3x) = 4 sin(x) cos2(x)

A:

Q: Verify the identity sin(+e) - cos e

A: Given : sin ( 3π/2 + θ ) = - cos ( θ )

Q: Verify the identity. cos 3x 1 csc x-2 sin x 2 sin 2x

A:

Q: Verify the identity. cos (x+ n) = - c COSX

A: It can be varified using the formula for cos(A+B)

Q: Verify the identity. 2 cs" e 1-- 1+ sin 0 = sin 0

A:

Q: Verify the identity : sin 4t = 4 sin t cos3 t - 4 sin3 t cos t

A: Verify the identity : sin 4t = 4 sin t cos3 t - 4 sin3 t cos t

Q: Factor  Cos^4 x + 2 cos^2x + 1

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Q: Verify the identity. 4 cos?(x) – 2 = 2 – 4 sin2(x)

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Q: (b) cos x = 0.549

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Q: 1-x2 – x² Differentiate cos with respect to x. 2 1+x?

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Q: 24. Prove the identity 1 – (sin x – cos x)2 = sin 2x

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Q: 1. Use an identity to find the value of cos (0+ 90°). sin 0 cos 0 O - cos 0 O - sin e

A: We have to find the following

Q: 1. Find the exact value of cos 7x/12

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Q: 1 cos²(x) 2

A: The given question as belonging to the calculus in which we have to find the given integral so now…

Q: Write a formula for cos 2x by writing cos 2x as cos (x + x) and using the formula for the cosine of…

A: cos2x

Q: Verify the identity: [cos(x + h) - cos x]/h = cos x. (cos h - 1)/h - sin x. (sin h)/h

A: we have to verify the identity : cos(x+h)-cosxh=cosx(cosh-1)h-sinx(sinh)h

Q: Scos ()"00s (2x) x Cos (X

A: To evaluate the indefinite integral

Q: Find the value of cos-1(2) using Euler's formula.

A: We find cos-1(2) , by using Euler's formula.

Q: rsec(x) 3 cos(x)dydx * JO -

A:

Q: Rewrite cos x in terms of sin() and cos(x) 4

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Q: |2x cos (x² -5) х cos

A: To find value of ∫2xcosx2-5dx Solution: Let substitute t=x2-5 Differentiating both sides with…

Q: 1- cos 0 1+ cos 0 sin 0

A:

Q: a/2 -6 cos (x) dx

A:

Q: x) - 0.5 cos(x)) on the

A: Given as, f(x)=e-x3.2sinx-0.5cosx in the interval [3, 4].

Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.