a) Differentiate f(x) = sin x from first principtes. %3D

Q: Solve the DE: tan xsin y y'+(3 tan x-2 cos y) sec x=0

A:

Q: find x,sin(2cos-1(cot(2tan-1x)))=0

A: Given: -

Q: Obtain the general solution to the equation dr +r tan 0 de sec 0.

A: Given first order differential equation is drdθ+rtanθ = secθ. We have to find general solution of…

Q: 11. y = sin 12. y = cos*(-) 13. y = arccos(-) %3D 14. y = arcsin (- 5

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Q: Find y'. Given: y = -sin(4x)cot(4x) %3D

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Q: • y = sin¬(10x) %3D

A:

Q: 5. Find the values of a and b such that dx tan 1 + sinx a + b . %3D

A: We need to integrate ∫11+sinxdx

Q: 3.§ sin* 2 x sin 4 xdx

A:

Q: 2- Evaluate sin x dx usin i. Trapezoidal rule ii. Simp

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Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

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Q: L[sin bd]- show that

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Q: 10) Find the equation of the line tangent to the graph of tan x at a) x = 0 b)x = " c)x = %3D 4 sec…

A: We can find answer to question no 10 as below.

Q: 5. f sin x cos x dx

A:

Q: Suppose y = sin x. What is the x- value between 0 and that corresponds to a y-valué of ? 2 [?]

A: The objective of the question is determine the value of "x" where as y=1/2 in the given function…

Q: eliminate the arbitrary constant y = sin ax

A:

Q: 6. f cos¹ 2 xdx

A: Given,  ∫ cos7 2xdx

Q: find the derivatice of y=sqrt[sin(x^4-1)]

A: Consider the given equation

Q: 11.J sin 3 x sin 6 xdx 3

A: To evaluate the given integral.∫sin 3x sin 6x dx

Q: 2. Find [cot (x)sin* (x)dx

A: First simplify then integrate

Q: Evaluate the inclepinite infegral Cos 3X +3 dx Sin 3x

A:

Q: 1. Find of the trigonometric function: dx y=−10x + 3 cosx

A: Derivative of Cosx is -Sinx

Q: Find the trigonometric integral ∫x tan4 x2 dx

A: Given: I=∫xtan4x2dx for evaluating given integral, we substitute  x2=t…

Q: 2x – sin y y' = x cos y

A:

Q: 9. Express tan 0 in terms of sec 0 for 0 in Quadrant II.

A: We know that, sec2θ=1+tan2θ So sec2θ=1+tan2θtan2θ=sec2θ-1tanθ=±sec2θ-1 But given that θ lie in…

Q: In cof '3x sinAte ech x² 2

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Q: Differentiate y = sin 20 cos 20

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Q: 9.f tan3³ x √sec x dx

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Q: 2 2. cos² ydy 1+sin y

A: The given integration is: I=∫cos2y1+sinydy   We know the common integral. ∫sinxdx=-cosx+C

Q: Differentiate  (sin 2t)/t.

A: ft=sin2tt

Q: 2x y = Arc sec 3

A: We will use the formula of derivative of arc secx to solve this question.

Q: sečxdx ztanx 5-9tarix ansi sin 2

A: Solution is done in step 2

Q: Discuss the similarities and differences between y = sin 0 and y = csc0 %3D %3D

A: Given: two functions- y=sinxy=cscx

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

A:

Q: S sin x In(1 + sin x) dx

A: Given : Integral of sinx ln(1+sinx) dx The genral formula for the integration of function is as…

Q: S cos3 x sin* x dx

A:

Q: 6. Se¯*tane¯*sec?e¬*dx

A: To evaluate: I=∫e-xtan(e-x) sec2(e-x) dx=∫tan(e-x) sec2(e-x) (e-x)dx...(1)

Q: The x2-4 dx can only be evaluated using trigonometric substitution technique. A True False

A:

Q: Evaluate the intergrals. ∫ ex sin2x dx   show the complete solution. step by step

A: There are exponential function and trigonometric functions in the product in the given integrand.…

Q: Recall that cos 'x = arcas x. find %3D 1/2 X sin(cou-x) dx

A: Answer

Q: Compute / tan x · sec a dæ.

A: detailed solution is given below

Q: Show that: cos hz = cos hx cos y + i sin hx sin y.

A:

Q: 1. f(1-cot 2 x)² dx

A: Solution:

Q: Eoaluate dx, Hence find the value of sin dx.

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Q: 16. S cot xdx /1 + In sin x

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Q: To approximate the value of sin44° , we will use y=sinx. What must be the yalue of dy ?

A: the aproximate value of sin44 = 0.6946 for approximation  let  y= sinx dy = cosx(dx)             x=…

Q: Differentiate: y = (e2x)/(sin(2x))

A: We have to differentiate the function: y=e2xsin 2x Here two function are in ratio so we should use…

Q: What is d/dx sin x ?

A: To find the derivative of sinx (ie) To find ddxsinx

Q: Determine the period as requested. 5) Feriod of y 5 sin 4x A) 4 C)2 -1/2

A: In this question, we want to find the period of the given function.

Q: 3. Find the equation of the tangent line to sin- (x – 2y) = 2xy- 1 at the point ( 1, ;).

A: We will solve the problem