Use the substitution u = sec x to evaluate tanx sec x dx 1 -sin 4x + C 32 -sin 2 x + + + C 1 sin 4x + C 32 + -sin 2x– 4 -sec'x + sec x + C + C sec'x 3x - sec x + C

Q: 2: Prove that a) cosx tan3x = sinx tan’x b) (sin x + cos x)² = 1 + sin 2x

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Q: Find the minimum value of ∣sin x + cos x + tan x + cot x + sec x + csc x∣ for real numbers x.

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Q: 4. Verify. COSX 1+sinx = 2secx %D а. 1+sinx COSX b. cosx(1+ tanx)² = secx + 2sinx %3D

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Q: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

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Q: prove that tanx V secrsinxtanx

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Q: Prove that: 1) csc 0 + tan 0 . sec 0 csc 0.sce20 1-cos" x 2) sin x .cos x tan x 3) 3 cos' x-sia x+1…

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Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: find integral tan 5 x sec 7 x dx

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Q: 2 tanx + 7tanx+ 5 sec2x 2 tanx + 5 X. %3D

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Q: prove tany csc3-tanX =cos x CSCX Sinx tanx tcosX-

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Q: 1/tanx+secx=cosx/sinx+1  verify

A: We simplify the left-hand side first. Multiplying by (secx-tanx) in numerator and denominator.

Q: 7/3 x tan (x) dx 2

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Q: Find tanget line to f(X) =tan(X) + 9 cos( X) at X=π

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Q: Verify. a. (2 tan x ) / (1 + tan2 x) = sin(2x) b.  1 / (1 − sin θ) + 1 / (1 + sin θ) = 2 sec2 θ c. 1…

A: Part a)Given:

Q: tan°(x) sec²(x) dx = 1/7tan^7(x)+1/9tan^9(x) %3D

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Q: f(t) = In Itsinx 1-sin x g(x) = x sin ¹3x + √1-9x² G(x) = x In (9 + x²) + 6 tan-¹ (-)-2x

A: Note: Since, in the first function there is a typing error "f(t)", it should be "f(x)" because it is…

Q: 1 Differentiate f(æ) = sin-(4x). Use exact values. = (x),f

A: We use the chain rule for differentiation

Q: evaluate fsin.x dx inx dx JT+sin x A secx- tanx - x +C B secx + tanx +x+C C) secx + tanx - x + C

A: Here we have to evaluate, I=∫sinx1+sinxdx

Q: 1. f(cos 3x - x²) (sin 3x- x³)5 dx 2. f cos² x (tan x) (sec² x − 1) dx 3. f tan x (sec² x - 1)(sec²…

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Q: Prove (Start either from the LI 1- sin x 2. cosx COSx 1+ sin x

A: To prove : 1-sinxcosx=cosx1+sinx

Q: (sinx + cosx)^2 = 1+sin(2x

A: Consider the given expression sinx+cosx2

Q: integrate (sin(x)*tan(x)-cos(x))/tan (x+1)

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Q: Verify the identity tan(x) Cos(x) csc(x) (1 sec(x)) 1 1cos(x) 1cos(x) tan(x) cos(x) tan(x) 1 -…

A: Given identity to be verified is

Q: verify that (sin(x)-cos(x))^2=1-sin(2x)

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Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: If f(x)=tan x, then show that f(x+y)-f(x) = sec^2x tany/ 1-tanxtany

A: The detailed solution is given below Thank you

Q: HW/ Prove that: (1) 1-tanif x sechx

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Q: prove that = - Cotx + C 1- cosx +Sin'x

A: According to the question, we need to evaluate the integration: F(x) = 2(1 - cos2x + sin2x) We need…

Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Verify the identity: [sin 2x + (sin 3x + sin x)]/[cos 2x + (cos 3x + cos x)] = tan 2x

A: Consider the identity, sin2x+sin3x+sinxcos2x+cos3x+cosx=tan2x To apply the trigonometric identity,…

Q: Prove 2tan x cos (3x) = sec x (sin(4x) - sin (2x))

A: Topic- trigonometry

Q: Verify the identity. 2 tan(x) 1 + tan2(x) 2 tan(x) sec2(x) sin(2x) 2 tan(x) 1 + tan?(x) 2 sin(x) .…

A: The prove that  (2tanx)/(1+ tan2x) = sin2x

Q: prove that catX+c - Cos'x+Sin2X

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Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: Find f'(x), if f(x)= tan² 4.x. Find f'(x), if f(x) = sin² 2x./cos 2x . Find f"(x), if f (x)= Inx+…

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Q: Prove (secx+tanx)/(secx-tanx) = (1+2sinx+sin^2x)/cos^2x

A: To prove that   (secx+tanx)/(secx-tanx) =(1+2sinx+sin2x)/cos2x

Q: (1+ tan(z)) sec² (x) dx

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Q: 10. f cos*x sin x dx 11. (sec² 3x) dx / (tan 3x) 12. Setan 2x sec² 2x dx

A: Topic:- integration  Note:- as per our guideline if more than three subparts posted than only first…

Q: Prove the identity. sec (-x) – sin (–x) tan (–x) = cos cosx

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Q: What is the integrable form of sin-cos-sin0 do 2 2

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Q: Integrate (tanx)^3(secx)^3

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Q: Differentiate the following 1. g(x) = x³ cos x 2. g(x) = 4 sec x + tan x sinx 3. g(x) =- 1+cosx tanx…

A: 1) g(x) = x3cosx2) g(x) = 4secx+tanx3) g(x) = sinx1+cosx4) g(x) = tanx secx5) g(x) = x1+sinx

Q: (b) Verify that f(x) = 2 cos(x) sin(x). f(x) = sin(7x) + sin(8x) 7x + 7x = 2 sin 2 = 2 sin |co(-)

A: Let the function is  f(x)=sin(7x)+sin(8x)   Formula used: Sin(a)+sin(b)=2sina+b2cosa-b2

Q: secx-11-cos.x sinx secx +1

A: We have to prove

Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

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Q: Show that:- tan-1 x + tan-1 y = tan-1 x+y 1-ху

A: We need to show the following identity tan-1x + tan-1y = tan-1x+y1-xy

Q: Prove that _ d tanx = Sec'x.

A: