Prove the identity. cof(x+ 풍) + ain(x-) -。 Use the Addition and Subtraction Formulas, and simplify. cod( x + =) + ain(x - =) - (cont)(L cos(x) sin sin(x) cos(x) cos(x)

Q: 2. Prove the identity: (cos x- sin x)2 + (cos x + sin x)2 = 2. %3D

A: To prove  that cosx-sinx2+cosx+sinx2=2

Q: Prove the identity. cos(x-y) / cosx cosy = 1+tanx tany

A: To Prove:cosx-ycosxcosy=1+tanxtany

Q: 11. Prove the identity sin x 1+ cos x 2 csc x 1+ cos x sin x

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Q: Hiw ABy using Euler's formula prove That : sin(-2)= cosz

A: Euler's formula  Sun(a-b) = sinacosb - cosa sinb

Q: True or false? Explain/Prove. 3. For any neN, dx+n dan [cos(-x)] = (-1)2n cos (-x).

A: Given query is to find statement is true or false.

Q: 3 sin° x -dx Evaluate ' cos° x

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Q: Verify the identity: cos2 x - sin2 x = 2 cos2 x - 1

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Q: If e/2i -/2i = sin2 then z = - 2i In(sin2) – 4kn 2i In(sin2)+ 4kT - 2i In(sin2) + 4kTt

A: Given: e-z2i=sin2

Q: Setting x= cos or cosho show that Tn(x)==[(x + √X²_₁ )² + (x-√x ²₁ ²]

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Q: Prove the identity. 3. cos X sim x= 2. S1in X-Sin x) COSX

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Q: Evaluate sin (; - i In v2) cos(; - i In i ln v2) i In /2) cos o (3/4)i o (3/8)i o 5/8 o 5/4

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Q: Q3) Use the addition formulas to derive the identity of (cos (x --): sin x ) %3D

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Q: proof 1)  (sin x + cos x)2 = 1+ 2 . sinx . cosx 2)  cos4x - sin4x = cos2x - sinn2x

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Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: (4) Prove the formula cosh x - sinh2 x 1 using the methods in this workshop. In other words, express…

A: Consider the given identity

Q: 5. cos A =- and sin B =, both A and B in QIl. 6. cos A = - and cos B = - 2, with A and B in QIII. 17

A:

Q: III. Verify the identity. 5.) 1-Cos 2x tan?x %3D 1+ cos 2x

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Q: 1) VERIFY THE POWER REDUCING FORMULA, cos"x : cos 2x+1 HOLDS TRUE FOR 2 x = - AND x =

A: To verify:   cos2x=cos2x+12, for x=π3 and x=π2   NOTE: As per our answering guidelines, we can only…

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: *k) 1- (sinº x+cos x) = 3 sin² x cos²x

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Q: sin(2x) 1 Prove the following identity: cos(2x) - 1 - tan(x) sin(2x) %3D cos(2z) - 1

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Q: 12. Evaluate Cos 0 -sin & - Bin sin 0 Co3 0

A: Given: cosθ−sinθsinθcosθ4

Q: e identity: cos 3x = 4 cos x-3 X So

A: # we are entitled to solve one question at a time please resubmit the other question if you wish to…

Q: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

Q: Q/prove that : (cos x) = -Sin X %3D

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Q: Prove: sin? x 2 cos“ = cos 2-2cos x

A: We will use basic properties of trigonometric ratios

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: Theory and Examples

A: limx→02x23-3cos x

Q: Show that cos bx = (eibx +e-ibx) and 1 sin bx :(eibx – e-ibx). 2i

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Q: 2. Prove the identity: cos (x-y)– cos (x+y) = 2 sinx siny

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Q: 16. Establish the identity: os 0)² + (sin 0- cos 0)2 = 2 %3D

A: We need to establish the identity  (sinθ+cosθ)2+(sinθ-cosθ)2=2

Q: sin(cos (0.5354)) = O 0.8446 O 1.8446 O -0.1554 O -1.1554 O 2.8446

A:

Q: 1. Evaluate (3260)"]" × (-5+ j6) (cos(3 + j5)]1-/) Sin sin-

A: We have to find: sin-13∠60°3*×-5+j61jcos3+j51-j. We will find the interior parts first on different…

Q: Describe what is wrong with the simplification shown. cos x - cos x sin^2 x = cos x - cos x (1 +…

A: Just simplyfing the above question we have

Q: 1) Prove that cos°(x) + sin (x) = 1. (refer to notes). Use the "Square" formula.

A: See the attachment

Q: Prove the identity. s (xxy) sinx- sin (x-y) cosx= siny cos

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Q: Prove the identity: sin(0)-co sin (0) +cos (0)–1 cos (8)+1 sin(0)+1 cos(8)

A: On proving this we will get

Q: cosxtanx - cos x= 0 + O 0+n,+ 2nx 5я O O+*5, + 2nx 5я

A:

Q: Evaluate the limit of x —> negative infinity. Cos (2x) / x+25

A: To find limx→ -∞ cos2xx+25

Q: lim,-o-cos(2.x) →0°sin²(3x) Q6- Evaluate:

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Q: sin 2x sin x Cos 2x %3D Prove that 4 cos x - sec x Cos a

A:

Q: Evaluate sin (4x + 14) dx cos (4x + 14) Ocos (4x + 14) + C O-cos (4 + 14) + C -cos (4x + 14) +C…

A: Integration

Q: lim 2?e --00 1- cos(2x) im

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Q: (a). Find a common denominator for COSX |- COSX and 1- COS x COS x –COS X COSX = cosx-coseX COS X…

A: a To find a common denominator for 1cos x and cos x1-cos x.b To expand cos x+tan x2 and to simplify.

Q: sin(k/n), lim is 1. cos(1) +5/3. 2. cos(1) + 1/3. 3. cos(1) +2/3 4. cos(1) - 1/3.

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Q: tx)+ Sin(꼴-)- -26S X %3D Prove sin

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Q: 1. Evaluate 2. Evaluate sin(20) 30 x-2x cos x sin x limo lim, 0

A: Given is  limθ→0sin(2θ)3θ. L'Hospital rule: limx→af(x)g(x)=limx→af'(x)g'(x) NOTE: According to the…

Q: Form the differenti al equati on by eliminating the arbitrary constants A and B from the equati on y…

A: Here we have the equation  y = ex (A cos x + B sin x)

Q: Verify the identity. sin (e + n) = -sin e A) sin (e+x) = cos Osin e- cosa sin a = cos Osin e--0 =…

A: