1. Match th A. Sin В. Cos С. Tan

Q: The value of 1 cos (tan ¹y) + y sin (tan¯¹y) cot (sin¯¹y) + tan (sin¯¹y) is......... +y¹

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Q: Siven cos x E and π x<. 5 ", find tan(2x) %3D

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Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: 04.) Show that y= (sin x +cos x) sec x = see? x

A: Use the trigonometric identities and simplify to prove the given expression. Also check for a value…

Q: a L{sin at} = s2 + a?

A: We have, Therefore,

Q: Suppose y = sina, which is TRUE about y? 1 Oy= sin O none of the above y 0 *= arcsing O * = sin y

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Q: Show that if z = x+ iy, then: | cosh-z|2 sinh x Hint: use the equation: | coshzf = sinhx+ cos"y

A: We have , z = x + iy We know that ,  coshz = ez + e-z2 Therefore , cosh (-z) = e-z + e-(-z)2 = ez +…

Q: Q.5/ Show that sin(z) = sin(x) cosh(y) + i cos(x) sinh(y)

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Q: (a) The averages of cos x and lcos x| from 0 to x are (b) The average of the numbers v,, the average…

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Q: 1. Differentiate the following with respect to the variable given. 1 cosx 2 sin' x tan

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Q: 5) find the awnsers Sinh x = 39/80 Cos h x = ? Tan h x = ? Cot h x=? Sech x=? Csch x=?

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Q: 1 lim is equal to: (t – 1)2 '

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Q: Assume that a particle’s position on the x-axis is given byx = 3 cos t + 4 sin t,where x is measured…

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Q: a. Y = cot(Ve“ ) tanh(e") -1 (sin(x²)) tan(2²) tan(ray) = x + y? b. y = C.

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Q: Verify the identity: (sin x - sin y)/(cos x - cos y) = -cot (x+y)/2

A: sinx-sinycosx-cosy=2cosx+y2sinx-y2-2sinx+y2sinx-y2=-cosx+y2sinx+y2=-cotx+y2…

Q: Determine the exact measure(s) of 0, where 0° < 0< 360°. and tan 0 = 0

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Q: W (1, sin x, cos x) =

A: Use formula for the wronskian is determinent form.

Q: S sin° (3t) cos(3t)dt Evaluate COS

A: To determine the value of the integral.

Q: 4. 70 30 Show work: trig ratio (sin, cos, or tan) of %= trig ratio: X =

A: sin 30∘=AdjacentHypotenuse=pq Here, p represents the adjacent and q represents the hypotenuse. p=x…

Q: Which of the following equations is equal to 1 A cosh (x) – sinh2(x) (B tanh²(x) – sech2(x) ©…

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Q: B) If sinh e V3 Find cosh 0, tanh 0, coth 0.

A: The function sinh(θ) is called the hyperbolic sine function. It is defined as sinh(θ)=eθ-e-θ2.…

Q: du nd az and " if z = 5 tan-'(x)and x = e" + In(v) at tl-

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Q: Q/ ind dy if 24-sini' (xe!)=sin'(x*)+ cos (x")

A: Given that      2y - sin-1(x2+1) = sin2(x4) + cos2(x4) Here we have to find dy/dx.

Q: Differentiate cos cos" Vi-x? y = ecos

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Q: [ san28 e tan 20 ,tan 28 sec 2 Bd

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Q: 40 a) Find sin' xcos' xdx by using substitution u = cosx.

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Q: 9. dt + 을 = COS t + Answer: s = sin t + 을..

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Q: d(tan(x)) Using Euler’ formula, show that dx cos x 1.

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Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: Establish each identity given in attachment.

A: To establish the identity: lntanθ=lnsinθ-lncosθ Solution: We know that, tanθ=sinθcosθ Property of…

Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: Y = = ecos(x) + cos(e*)

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Q: 13. et sin t, et cos t

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Q: 1 and tan(t) > 0, find sin(t) and cos(-t) 3 If cos(t) sin(t) = cos(-t) =

A: Given:cost=-13sint=?cos-t=?Formula:sint=1-cos2tcos-t=cost

Q: If: e = a and ey = b Find the value of tanh(x) + sinh(y) for a = 0.77 and b = 0.35 %3D

A: We will use the following formulas sinh(x)=ex-e-x2,  cosh(x)=ex+e-x2 and…

Q: 4 I sec(ø) (b) p* sin(ó) dpdódo

A: The answer of part b is as below.

Q: 22. Determine Sz sin? y cos y dy

A: Given that: ∫0π2sin2ycos6ydy

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

A: Answer

Q: 27 sin x cot xcosx dx = ? ^.cosx

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Q: :(3:+a- (メ+) tanx tHany 1-tanx tany to

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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Q: (1+cot 0) de 5. sin e4 - cote

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Q: Q7 tan (0) sec (0) de is equal to: sec (0) - 3sec (0) + C 3sec (0) +C 3cos (0) +C tan (6) sec (0)…

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

A: Topic  =trigonometry

Q: y = C, sin at + C2 cos at, (a not to be eliminated)

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Q: fip when r = 0, if given y = tan (sinh z). Find dr

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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: If sin-r= In y, show that UTM dy (1-2) = y. dr

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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.