Why does eix=cos cos x + i sin sin x ?

Q: Use the method of substitution to evaluate | 2x cos x² dx. sin x? + c – sin x? + c sin x? + c sin x-

A: We use substitution method

Q: 1 (5) 1- cose 1+cos 0 sin?0

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Q: Given that " = n, sin (x) dx 3 -T, what is 8 sin (0) de?

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Q: What is the equivalent expression of sin( −z) + sin(+z)?

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Q: Show that A" cos (ах ah + b) = | 2 sin cos a + bx +n (ah + T 2

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Q: Sketch the graph

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Q: Find tan'e de cos*e 33. sin o 36. Cos

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Q: The general solution of y 'tanx sin2y = sin?x + sin?y is

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Q: 44. Use the accompanying figure to show that sin-x dx. sin x dx y = sin y = sin x

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Q: 38. Differentiate y = 2 cos² - a. – sint b. - sin 2t C. - sin - d. sin-

A: Differentiate y=2cos2t2

Q: Express the given quantity in terms of −sin x or cos x. sin(3ℼ/2 - x)

A: The given trigonometric function is f(x)=sin3π2-x

Q: coso dz+ (2Z o)do= o sin © - Cos

A: Use exactness formula to check and then solve

Q: sin' (2t) cos? (2t) dt

A: Use the substitution and replace the terms by new variable and solve easily.

Q: Apply Newton’s approx. to find the value of x for cos x = sin x; x0 = 1.

A: Topic-  Numerical Analysis. Newton's approximation Formula: xn+1 = xn - f ( xn)f' (xn)

Q: y = cos( + sin(x))

A: Please refer the attached image for complete solution.

Q: Evaluate: / [cos(x) – sin(x) ]dx

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Q: sin(cos (2x)), where 0<x<

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Q: An equivalent expression to sin(-x) is: Oa) - sin(-x) b) sin(x) Oc) - sin(x) d) cos(x)

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Q: 4. Describe a way of evaluating x cos? x dx. sin' х. х со

A: We will use the reduction formula,  to solve this integral. where n ≥  is an integer. Now., we…

Q: If Sin (3x + 5) = Cos(2x – 10) what is the value of x?

A: Topic-Trigonometry

Q: Given that sin(x)dx = 2, find I = 3 sin(x +2 7)dx. ||

A: Given that: ∫0πsin(x) dx=2 To find I=∫05π3 sin(x+2π) dx

Q: In cof '3x sinAte ech x² 2

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Q: i sin°Hcos* () .3x, sin°cos* dx 10. 3 10

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Q: Se2* (sin x + cos x)dx

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Q: Find fo, fe fe if fp.0,4) p cos sin 0 %3D

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Q: state what method applies and how one applies it, but do not evaluate the integral:

A: Given integral is We will evaluate the integral by substitution method.

Q: Evaluate: " sin" () cos* () .4 CoS 2, dx .2.

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Q: ) Find | sin can) cas (ga)da cos (gx) dx

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Q: Example : Find S“ (cos ti + sin tj+ tk)dt

A: We can do integration w.r.t. dt

Q: We wish to compute sin° x cos“x dx,

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Q: b) SE cos(3x) sin(3x) 18

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Q: sin Tt cos Tt dt

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Q: find dr/ ds r cos 2s + sin2 s = π

A: It is given that,r cos2s+sin2s=πWe have to find drds

Q: Find Se2= cos(x)dx.

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Q: If Sin(3x+5) = Cos(2x – 10) what is the value of x?

A: This question is related to comparison of trigonometry function.

Q: (cos x) = –sin x dx

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Q: sin 2x dx 1+ cos? x

A: Given : ∫sin2x1+cos2xdx

Q: 0 sin√xcos√x √x dx is equal to

A: To solve the given integral

Q: Sz sin?m-10 cos2n-10 = – B(m,n) В (т,п)

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Q: What are the properties of y = cosθ and y = sinθ

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Q: If sin y° =  9/c and tan y° = 9/d, what is the value of cos y°?

A: We know that, tan y°=sin y°/cos y°, So, cos y°=sin y°/tan y°.

Q: What is the value of S(cos 1 + V1 +r? sin?t cos -=/4 cos'r) dt ?

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Q: What strategy would you use to evaluate ∫sin3 x cos3 x dx?

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Q: y = sin x coS X 4

A: Given data:     The given equation is: .   The given expression can be written as,

Q: Cos x [SND] If y = tan x+ seç show that, y = (1 – sin æ)?

A: Topic  =trigonometry

Q: 3 Cos |X TT 13) y = 3

A: We need to plot the graph of given curve:

Q: (11). - cos?(2y) sin? (x), y(등) =0 Workings y= tan '(z - 글sin 2v) +

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Q: If sin x + sin y = ½ and cos x – cos y = 1, find x

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Q: da (cos ( 3x) sin( 2æ)) dæ

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Q: Differentiate (sin(ax+b)/cos(cx+d))

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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.