(a) Compute the integral (b) Compute the integral sec Ode by observing sec 0 = sec (tan+sec 0) tan 0 + sec 0 se sec³0d by observing that sec² 0 = 1 + tan² 0 and using part (a).

Q: Let Express the value of in terms of I. pn/12 0 tan ¹2 (2x) sec (2x) dx I = p/12 10 S tan ¹0 (2x)…

A:

Q: Calculate value for  sin((j*pi)/2)

A:

Q: 8. Find the principal value of Arc tanh(1 + j2)

A:

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

A:

Q: 2. Explain why arcsin(sin(0)) = 0 but arcsin(sin(807)) # 807

A: Concept  arcsin(sin x) = x   is true  only when x lie in the interval [-π/2 , π/2]

Q: 1. Prove that the derivative of tan(x) is sec²(x) directly from the definition of the derivative.…

A:

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: B) prove du d 1. sec u = secu tan u %3D dx dx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the first derivative of y = Arc tan √x² −1+ Arc csc x 2 O 2 O 0 2 Ox√²+1

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

Q: 3 (a) Differentiate the left-side functions with respect to the right-side ones I+/(1+x³), i) tan…

A:

Q: Find the derivatives using Trigonometric Functions 4 y = cos* t – sin* t \1/2 ソ= v = (2 tan² 20 –1)"

A:

Q: Find, tan(x / 2)dx A) (1/2) sec (x/2)+c C) 2 sec (x/2)+c B) 2m sec(x/ 2)+c D) (1/2n sec(x/2) +c

A: Given that a integration of tan(x/2) and we solve it by using general formulas of integration. We…

Q: The value of i log (x -i) + i? n + i³ log (x + i) + i* (2 tan-'x) where x > 0 and i = Fis

A: Introduction :

Q: 16) Prove the 1+ tan?(u) = sec2(u).

A:

Q: etermine the form that would make f sin () cos () sin(0) de

A: We have to determine the form of the given indefinite integral

Q: Compute tan" z · sec² æ dæ. O tan12 z tan10 z +C 12 10 O tan° a tan10 a +C 10 tan12 a sec æ +C 3 12…

A:

Q: (a) sec¹ (31) √tan(3t) dt

A:

Q: Expand tan(x) in powers of x up to first six terms and estimate the value of the function with x…

A:

Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric  function properties

Q: 1+tanx b) 1-tanx = tan (x + ²)

A: