Prove the following identities: 1- sin x cCs x 1. + - = 2 sec x %3D 1- sin x cos x

Q: 6. Verify each of the following identities: cosx (a) 1-sinx = secx + tanx (b) 2sec²x + 1+sin 1-sinx…

A: As you have asked for question d only. So I am solving that only. Thank you.   sec(x)*cos(x)=1…

Q: If S (x) = - sin(x), then f (11) (x) is equal to – sin(x) B B -cos(x) CosX sin (x) D O cos(x) A,

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Q: Prove the following Sin hZ=0

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Q: 3. Finish the proof of the following identity. sin'x+ cos xsinx cos x sin'x+ cos x sin x cos x tanx…

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Q: Find all values of x in the interval [0, 2?] that satisfy the equation. 6 cos(x) + 3 sin(2x) = 0

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Q: Prove the following inequalities (ii) -10|< sin 0 < |0| and -|0| < 1– cos 0 < |0|

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Q: Differentiate the following function COS T 1 (a) sec(x) tan(x) (b) (c) sin (4x° + cos(x))

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Q: Prove the following identity: sin(21) 1+ cos(2x) tan(z) 1

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Q: Express the given quantity in terms of sin x and cos x.

A: Express the given quantity in terms of sin x and cos x.         cos3π2+x

Q: 103. Prove that for all whole numbers n > 1, sin x = sin (x + d" dx" Hint: Use the identity cos x =…

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Q: Prove the formula eix cos(x) + i sin(x) %3D Use this to evaluate e2i

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Q: 5. Assuming that (d/dx) (sin x) = cos x and (d/dx) (cos x) = - sin x, prove each of the following. d…

A: The quotient rule of differentiation states that uv'=u'v-v'uv2. (a) Write cot x=cos xsin x and use…

Q: 8. Show that sin a (1+ tan a) + cos a (1 + cot a) = sec a + csc a.

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Q: Prove the following identity: 1-cos x sin x sin x 1+cos x

A: To prove: 1-cos xsin x=sin x1 + cos x Use the trigonometric identity, sin2x + cos2x = 1

Q: Prove the following identities: sin 6+ sec 0) +(cos 0+ sece) = (1+sec0 cosece)

A: We can easily prove this given identity shown below

Q: Evaluate the following 1. S sin x sin (cos x) dx

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Q: snip

A: Our Aim is to establish the identity given below:-1-sinθcos (θ)=cos (θ)1+sinθ-(i)

Q: 1. Use the Intermediate Value Theorem to show that there is the solution to the equation cos(x)=x in…

A: Given cosx=x

Q: Find the root of f(x) = e −x (3.2 sin(x) − 0.5 cos(x)) on the interval [3, 4] up to 1 d.p.

A: Consider finding the root of f(x) = e-x(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

Q: Compute the following: sin² (x) dx

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Q: Let y = In (cos x). Which of the * ?following is dy/dx - tan x (In x)(- sin x) + (cos x)(In x) O cot…

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Q: 1 cos A 13. If with A in QIV, find A sec

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0.…

A: Sine function and it's continuity at 0

Q: Find 1+sin -cos I COS In | sin - z+cos In In 1+tan +C +C +C +C

A: We can evaluate the given integral by using the substitution u = tan (x/2).

Q: Ex2: Use the identities 4 and 5 to prove that: cos(x- y)-cos(x+y) (a) sin x sin y = 2

A: Formula used -  cos(A-B) = cosA cosB + sinA sinB  cos (A+B) = cosA cosB - sinA sinB

Q: Evaluate the integral ∫1/θ2 sin 1/θ cos 1/θ dθ

A: Given- ∫1θ2sin1θcos1θ dθ To find- The value of the integral. Concept Used-  The above integral can…

Q: is cos x = 1/sec x an identity

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Q: Verify the following identity sec(x)-cos(x)/sec(x)+cos(x) = sin^2(x)/1 + cos^2(x)

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Q: Prove the following identities. sin 3x v 3 sin x - 4 sin cSC X - 2 sin 3 sec x - 4 sin

A: Given query is to prove the identity.

Q: 7. Prove the following identities. sin x 1 + cosx 1- cos x a. 1-cos x b. 1 + cos x tan? %3D sin x II

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Q: 25. Assuming that (d/dx) (sin x) = cos x and (d/dx) (cos x) = - sin x, prove each of the following.…

A: Our Aim is to prove the derivative of the following:-(i) ddxtan (x)=sec2 (x)Proof⇒ddxsin (x)cos…

Q: If S(x) = - cos(x), then s ()(x) is equal to A – sin(x) - cos(x) В sin(x) cos(x)

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

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: Prove the following i. ii. 1- sin x 1 = sec x – tan x. cosec e + sin x, V(1 – cos? 0)

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Q: Which of the following is equal to f(x)dx where S(x) =- sin(x) if 0<x< a/2 l cos(x) if 1/2<x<a } -2

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Q: 4. Verify the following identities: a. sin 3x = 3 sin x-4 sin3 x b. 1+ cos 10x = 2 cos? 5x %3D

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Q: Prove the following identities. sin 2x csc x =

A: Topic:- trigonometry

Q: Graph each of the following from x = 0 to x = 2pi  y = 2 cos 4x cos x + 2 sin 4x sin x

A: Given: y = 2 cos 4x cos x + 2 sin 4x sin x

Q: 2. Prove each of the following using identities, showing all work in the process. a. cos (x +) +sin…

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Q: 1 tan 0+ 1 sin 0 sin (90° – 0) tan 0 -

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Q: Enter the exact value of each when 0 = 1 - T. 6. sin(0) = cos(0) = %3D tan(0) sec(0)

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Q: given f (x) = 3/5 cos (6x), what is the largest possible value for f (x)?

A: Given query is to find the largest possible value of the function.

Q: 17) Prove the following: a) (sin x)(sec x)(cot x) 1

A: Since secx=1cosx  and cotx=cosxsinx Then LHS =  sinxsecxcotx=sinx1cosxcosxsinx

Q: Find z where z = sin (æ²) cos (4²) COS

A: The given function is z=sinx2 cosy2.

Q: Which of the following is equivalent to [sin(-x) + cos(-x)]? 1 - 2sinxcosx O 1 O 1+ 2sinxcosx O…

A: Use Trigonometric identities and simplify.

Q: 5. Integrate the following and show all of your work: sin“ r cos r dr

A: we have to integrate the following

Q: 5. Prove the following Identity: sin(2x) 1+ cos(2x) tan(x)

A: Use the following identities to prove  the given  identity. sin²x+cos²x=1 cos(2x)=cos²x-sin²x

Q: Show that : |sin x |= CoS nX Σ n2 even 414 2/7

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Q: Suppose v is in the interval (G, T ), with tan v = –3 Find the exact expression for the indicated…

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