3. Are reduction formulas needed to evaluate sin x cos? x dx? Why or why not?

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: Suppose csc(x)= = √43 A 5 34 B 5 43 - 5 -√34 5 √34 and cos(x) <0. What is the value of sec(x)?

A: This question is related to trigonometric ratios, we will solve it using given information.

Q: Find all solutions for tan (x) = 0. %3D 1 5 If sin (x) 0 <y<5, evaluate the expression CoS (x – y).…

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Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

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

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Q: Evaluate / cos“(x) sin³(x)dx. Include "+c" in your answer.

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Q: 40 Using the reduction formula, we have! sin"xdx = %3D

A: Given : ∫sin40xdx

Q: How is the addition formula used in deriving the formula (sin x) , = cos x?

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Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

Q: + C,? What should be the value of A so that f A : sin (6x²) dx = - cos(5x-) %3D 4 A. x С. Зх В. 2х…

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

A: Please refer the attached image for complete solution.

Q: If csc(z) = 6, for 90° <z< 180°, then %3D sin () %3D «(금) cos tan(플) - ||

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Q: which of the following is equal to į sin x cos (x) dx ? A cos () + C 3. cos (2x) + C O Option 1…

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Q: | cos ?x sin'x dx can be evaluated by factoring sin'x as (sin²x) ²sinx and transf sin²x into 1-…

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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: How would you evaluate f cos?x sin x dx?

A: We need to evaluate, ∫cos2xsin3xdx

Q: (a) sin(rxy) = x + y?

A: I am going to solve the given problem by using some simple caculus to get the required result.

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

A:

Q: 3. If cos x = 5 Find the sin x and tan x in the interval 13 xe 1]? X€ ,π

A: Given that: cosx=-513and x∈π2, π

Q: Given that sin-(x) = a and cos-(x) = B show that sin(a + B) = 1. %3D

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Q: 8. Evaluate sin (x) cos(r)dr using an appropriate substitution.

A: here  we use the formula  ∫(xn)dx=xn+1n+1+C     according to our guidelines we can answer only…

Q: Using appropriate substitution, ſ sin1º(x)cos³(x)dx is equal to: an

A: By using integration by substitution.

Q: Show that the two formulas are equivalent                                                      ∫tan…

A: To show that ∫tanx dx=-lncosx+C and ∫tanx dx=lnsecx+C both formula are equivalent. We know that…

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

A: To prove , or justify the identity exp(ix)= cosx+isinx

Q: Evaluate o (3 sin x – 5 cos x) dx.

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Q: Solve for the convolution of sin (t) and cos (t).

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Q: 16. Determine So sin x cos x dx

A: First simplify then integrate

Q: for what value of x is cosx 1=5cosx is true

A: Solution: Consider the given equation: cos x .1 = 5 cos x Therefore, 5 cos x = cos x5 cos x - cos x…

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: cos? y 1- sin y

A: sin2x + cos2x = 1

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

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

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Q: what is the derivate of sin(x)cos(x)?

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Q: What mathematical result is applied to prove that sin^2(e)+cos^2(0)=1?

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Q: Evaluate: [e* 1+ sin 2x dx 1+ cos 2x

A: Topic:- Integration

Q: sin (x) = 0.8. If x and y are complementary, what is cos (y)?

A: In the question it is asked to calculate the value of cos(y) for sin(x)=0.8. It is given that x and…

Q: If fx= cos³4x Sin 4x,then F(x) + C is ?

A: Consider the given function. fx=cos34xsin4x Now, find the integration of the function.…

Q: If cos x= √7/4 and 3 π/2 (less than) x (less than) 2 π, find tan x/2

A: If cos x= √7/4 and 3π/2 &lt; x 2π, find tan x/2

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: If x is measured in degrees and f(x) = cosx, then d f(x) = − sinx

A: To write that it is true or not.

Q: Using a suitable substitution, (sin x cos“ x) dx can be 4 (A) - f u*du (B)

A: Given: ∫0π2sinxcos4xdx

Q: Is this: sin x cos y- cos x sin y/ cos x sin y reciprocal quotient pythagoreom  algebra

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Q: 3 Evaluate cos x sin x dx.

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Q: dr + r tan 0 = cos? 0, do = 1. 4.

A: Given DE is drdθ+r tanθ=cos2θ   and rπ4=1 solve the given DE

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - cos(x) > 0 3 sin(2x) =D…

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Q: If r(0) = tan(sin 0), then r'(0) is:

A: We have given  rθ=tansinθ r'θ=drθdθ r'θ=ddθ(tan(sinθ)) r'θ=sec2(sinθ) ddθsinθ r'θ=sec2(sinθ) cosθ…