35-38 - Algebraic Expressions Rewrite the expression as an algebraic expression in x. 35. cos(sin'x) 37. tan(sin'x) 36. sin(tan'x) 38. cos(tan'x)

Q: b. cos ( I1/2 -x) c. cos(x+ II/2) d. tan(x+ II/2) e. tan( II/2 -x) a. sin ( I1/2 -x) 16. sin x 15.…

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Q: sin? x 1- 1-cos x =-COS X

A: Here we have to use the basic trigonometric identity sin2θ+cos2θ =1 and we know that  a2-b2=…

Q: Verify the identity.

A: Here we have to verify the identity,

Q: cos x- senx = cos4 x - sen x tan e tan a-1 tan a-coto (sec x + 1)(sec x-1) = tan?x

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Q: 4. cos*x Evaluate: sin' x( sin' 3/5 x+ cos³ x 3.

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Q: 2-tana 11. If Sin(x+ a) = 2Cos(x - a); prove that : tan x = 1- 2 tan a

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Q: 11 csc2 (-0) tan 0 cot(-0) Establish the identity: - sec2 e

A: Given,

Q: 1-cos x 2 Establish the identity: = csC x + cot sin x - sin a Cos x

A: Identity can be defined as the statement or equation that holds true for all conditions.In an…

Q: cos x-cos(5x) Prove identity: tan(2x) sin x+sin(5x)

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Q: tan x-1 3. tan x - 1 sin? x +3 sin x +2 4. sin x +2

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Q: Find the limits

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Q: cos²x 6. 1+ sin x = 1- sinx tanx - сotx 7. sec'x - csc?x = sin xcosx 8.1 tin cos2x = cscx - secx…

A: We have to verify that the given trigonometric identity.

Q: 1. Verify the identity. Show all steps. sin x tan² x-sin x = tan x (tan x – 1) cos x sin x+cos x

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

Q: 3 lim 2 x2.tan=.sin- X-00

A: We have to evaluate limx→−∞x2⋅tan2x⋅sin3x It can be written as…

Q: 4. Find the exact value of cos *x- sin "x-cos (2x). 4 cos x- sinx- cos (2x) = (Simplify your…

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Q: 1-cos(2x) sin²(3x) tan x-sin x Evaluate: a- limr-0* b- lim sin³x

A: (a) Given, Simply fie the above expression, On applying the limit, the solution is in 0/0 format.…

Q: sin 3x Prove the identity 4 cos x- sec x. sin x cos x

A: To proove: sin3xsinxcosx=4cosx-secx

Q: sin x - cos x = 1/5, what is (sin x) (cos x) equivalent to?

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Q: 1-cos(2x) - Evaluate: a- lim,-0 sin²(3x) tan x-sin x b- lim sin3x

A: According to L'hopitals rule,limx→af(x)g(x)= limx→af'(x)g'(x)iff(x)g(x)= 00or ∞∞. If there is any…

Q: 7) tan' x sin' x - tan' x-sin' x

A: (tan2x)(sin2x) = tan2x - sin2x

Q: 1- cos () 1- cos(x) 1- sin°(;) 1+ cos(x)

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Q: 10. Simplify (cos x- sin x)? - (sin x-cos x)'.

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Q: sin20 6. ) lim tan³0 0- 4

A: Given: limθ→π4sin2θtan3θ

Q: True or false sin* x 4 sin x cos x dx 4 True False Reset Selection

A: Use the method of substitution.

Q: cos(-x) 1– sin(-x) 4 x It sin x COS x 4 8 csc x 8 sec x -8 csc x -8 sec x

A: Use trignometric ratio and identities:-

Q: 1. If tan x = -3 then tan (-x) =  2. If sin x = 0.3 then sin (-x) = 3. If cos x = 0.2 then cos (-x)…

A: Answer 1. We know that  sin(-x)=- sinx and cos(-x)= cos x  tan x= sin xcos xHence  tan (-x)= sin(-…

Q: 3 tan 0 tan' 0 Show that tan 30 = 1-3 tan? 0

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Q: 5. (Double-angle formulas) Prove that a) sinh(2x) = 2 sinh(x) cosh(x) b) cosh(2x) = cosh? (x) +…

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Q: sin x= 6/7, cos > 0, sin y = -1/5, and cos y < 0 How do I find sin(x + y), cos(x + y), and tan(x +…

A: Given that  sinx=67, cosx&gt;0,siny=-15and cosy&lt;0. We know that…

Q: 6. (a) Express cos (2 tan- ) (b) Express sin (2 cosx) as an algebraic expression in x. (c) Express…

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Q: f(x)=2cos^2 x-1 , 1-2sin^2 x , cos^2 x-sin^2 x and cos2x Make a comparison of the four expressions

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Q: Prove the identity. cos(x - 1) - sin(x + 1) = = 0 Use the Addition and Subtraction Formulas, and…

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Q: tan x- 1 1. tan (x - 45°) = tan x + 1 1- tan 0 2. tan (45° - 0) = 1+ tan 0

A: Basic trignometry problem

Q: Rewrite sin(x+π/6) in terms of sin x and cos x.   Enclose arguments of functions in parentheses.…

A: We know that        sin A+B =sin A cos B+cosA sin B           sin x+π6 =?         A=x…

Q: VERIFY THE IDENTITY

A: By half angle formula , we have

Q: cos x – 1.75 = -1 COS X sin(4x) = 2 – sin 4x 4 tan(2x) – 1 = 3

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Q: - sin( - a) + sin-x 元 Simplify sin sin(21- x) 지+ 2

A: Given: sinπ2−x+sin(π−x)+sin3π2−x+sin(2π−x)

Q: tan x= -4 and sin x is negative

A: Here tanx=-4we know trigonometric identity,sec2x=1+tan2xsec x=±1+tan2xsec x=±1+(-4)2sec…

Q: (1-cos(x))= (2-2sin^2(x)) from (-pi, pi)

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Q: cos 2x 25. cos x- sin x A sinx cos X cos x + sin x 2 cos x + sin x cos x - 2 sinx B 2 sin

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Q: sec2 (0) S tan (0)-484

A: To find out the integration.

Q: sin 3x 39.lim tan 6t 41. lim 50 sin 21

A: We will use the l'hospital rule to fine the limit of 39.  To fine limit 41. We will use the basic…

Q: Verify the identity. sin(-x)+cos(-x) = -sin x + cos x

A: We need to verify the identity: sin(-x)+cos(-x) = -sin x + cos x For this we need to have the graph…

Q: Rewrite sin(x+5π/6) in terms of sin x and cos x.   Enclose arguments of functions in parentheses.…

A: We have rewrite sin (x+5 pi/6) in terms of sin x and cos x

Q: simplify.

A: Given

Q: tan x- cotx + 2 cos? x = 1 tan x + cotx

A: tanθ =sinθcosθ cotθ=cosθsinθ sin2θ+cos2θ=1