Q4: Prove that: secx • cscx = tan x + cot x

Q: 5- Prove that a) tan x (csc x – sin x) = cos x b) 1+ sec?x sin?x = sec?x

A:

Q: b. Prove that 2cot (20) = cot(0) - tan(0)

A: To prove the identity.

Q: Find the area bounded by the trigonometric curves y=sinx and y=cosx from; x== 3.459 square units…

A: Area bounded by the curve .

Q: 2. True or False. The dx [Arctan(tan x)] = 1 for all x in the domain. ans. True

A:

Q: Prove that sec x dx = In sec x+ tan x +C.

A: Here the question is solving by using u-subsitution method.

Q: If y=tanx, Prove that Y™ 2 (Y²+1)(3+1)

A: We will find the required.

Q: The trigonometric integral fs sec² x (tan³ x - 2 tan7 x) dx is equal to

A:

Q: J 1 cot³ x O 3 2 dx = In | sec² x − 1| + C --- O 1 tan² x + ln | sec x + C 4 O 1 2 O 1 2 1…

A: I have stated the used formulas in the solution

Q: a) cot x – tan x sec x(csc x – 2sinx) %3D b) cor y(sec²y – 1) = 1

A:

Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

A:

Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: 6. By using u = tan 0, evaluate | tan 0 sec*e de .

A:

Q: Q. Use first principle rule and proue that if y=s %3D secl tand = secx

A: Given: y=secx We know that for any given functiony=fx, first derivative is given by…

Q: Where does sin x have a horizontal tangent line? Where does cos xhave a value of zero? Explain the…

A: Concept: The function f(x) at the point x=a, is a line that just touches the graph of the function…

Q: V/ Prove that: (1) tanx= cot

A:

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

A:

Q: Let y=f(x)=sin^2(x)-cos(x)+2sin(x)+x find f'(x), factor f'(x) and determine the critcal values on…

A:

Q: If V(x)= In[sin(x)- cot(x)], find V'(x). %3D O a. cos(x)- csc-(x) sin(x) + cot(x) O b. cos(x)-…

A: Here we have, V(x)=lnsin(x)-cot(x) We have to find V'(x)=?

Q: Find f'(x) given トhat fcx)= tan Cax - Jx +4ょ3) %3D (assume real number) is

A: Our aim is to find f'(x) where f(x)= tan(ax5-x12+4x-3), where a isassumed to be a real number.

Q: evaluate using methods similar to those that apply to integral tanm x secn x.

A:

Q: What is the value of 4 (sin x tan dx X)? a) sin x + tan x sec x b) cos x + tan x sec x C) sin x +…

A: ddxsinxtanx= cosxtanx+sinxsec2x=sinx+tanxsecx

Q: ve f (cot x + tan x) dx then evaluate the an

A: The trigonometric square formulae state that: cot2x=csc2x-1tan2x=sec2x-1         -(1) The integral…

Q: D,(6 tan x) 6 sec² x sec² x (c) D,(In |6 tan x|) %3D 6 tan x 6 tan x tan x

A: Consider the given function as Dxln6tanx

Q: evaluate using methods similar to those that apply to integral tanm x secn x.

A: Given integral  By using the identity we get

Q: d -tan(z) = dz sec(x) O cot(x) O sec2(z) O

A: we have to find ddztanZ i.e we have to find derivative of Tanz with respect to z ddzTanz=sec2zdzdz

Q: HW /Prove that: (1) tanx=cot

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

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: the exprression csc x/sec x  is equivalent to: 1.  sin x 2. cos x 3. tan x 4. cot x

A: *to find:-  csc x/sec x = ?

Q: (b) Can we use the IVT to conclude that f (x) = tan(x) equals 0 for some c in (0, 1)? %3D

A: We can answer first question among which you asked as per the honor policy. please resubmit the…

Q: facR,af ischiffontiable at xo gisdiffera tible at to anol

A:

Q: Sa J (1+ In² sin x)5 “ cot x In sin x dx

A: Let the given integral be y - y = ∫cotx lnsinx1+ln2sinx5 dx           ..............(1)Let,u =…

Q: 2. Verify the following identities (a) sec 0- tan 0: sec 0+tan 0 (b) (cot z- csc z)(cos r+ 1) = -…

A:

Q: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

A:

Q: Given that = sec-(-V13/2), find sin x, cos x, tan x, csc x and cot x.

A:

Q: True or False: To evaluate the integral tan a sec" zdx, we save one sec z factor and use sec z = 1+…

A: Answer: TRUE

Q: Q. Use first principle rule and proue that secx tanl y = secx

A: Given : y=secx To prove : dydx=secxtanx using first principle. Proof : By First principle, we have…

Q: 5. Verify the following trig identities: A. secx tan x sin x = cos x B. secy_tany =1 cos y cot y C.…

A: The given query is to prove the following trigonometric identitites: secx-tanxsinx=cosx…

Q: (1+ tan(z)) sec² (x) dx

A:

Q: 1. tan x csc x-secx cot x sin x-cos x sin x cos x

A: This is a problem related to trigonometric formula. General formula which use for solving 1 problem…

Q: Show that tan(arccosx) for |x| s 1, x + 0.

A:

Q: Prove that sinh z = sinh x cos y +i cosh r sin y.

A: To prove, sinh z = sinh x * cos y + i cosh x * sin y

Q: sin z (sec z+1) cot r (1 – cos x) Prove

A:

Q: Find the area bounded by the trigonometric curves y=sinx and 2.828 square units 1.414 square units…

A: Given that curve y=sinx and y=cosx    from x=π4 to x=5π4To find :Area bounded by the region from…

Q: Use the substitution u = sec x to evaluate tanx sec x dx 1 -sin 4x + C 32 -sin 2 x + + + C 1 sin 4x…

A:

Q: 1. Which expression is equal to sec x tan z sin x using identities?

A: We can use simple trigonometric identities to solve the given equation.

Q: Q4: Prove that: secx * cscx = tan x + cot x %3D

A:

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

A:

Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

A:

Q: a. Show that y = tan u increases on every open interval in its domain. b. If the conclusion in part…

A: (a)  Given,

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.