1. Find the exact value of x if 0

Q: Find the indefinite integral ∫sin 5x sin 4x dx

A:

Q: EX / Show that cosh x-sinhx=1

A:

Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

A:

Q: Find the indefinite integral ∫sec5 x tan3 x dx

A:

Q: Use Newton Raphson method to obtain a root to 3 decimal places 1.   x^3-5x+3=0 2.   sinx=1-x

A:

Q: find integral tan 5 x sec 7 x dx

A:

Q: Prove sin 2x cot x (1 - cos 2x)

A:

Q: 10) lim TT X-- sinx-cosx - TT X- 4

A:

Q: Prove: sin (2 cosx) = 2x1-x

A:

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: Find the indefinite integral. ∫(sec 2x + tan 2x) dx

A:

Q: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

Q: Verify the identity sinh x + cosh x = ex

A: To prove the identity

Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: 16. Using the Quotient tanx= sinx/cosx to prove d/dx tanx=sec2x

A: Quotient rule of differentiation

Q: f6)= Sin () (x 3x26x-8) 1 CosX In Ceos x) | $66)=Sinx+t Cosx. sinsetl -6()=DSin -2053 2.

A:

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

A:

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

A:

Q: 3. sin(3x) = 3s in x – 4sin³ x

A:

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: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: cos“ xsin xdx X sin

A:

Q: sin 3x• tan 3x

A: Given integral,

Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

A:

Q: Find the indefinite integral

A:

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

A: To prove : 1-sinxcosx=cosx1+sinx

Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: Find the indefinite integral  ∫sin3 3x dx

A: Given: ∫sin33xdx

Q: Evaluate the in tegrol : S sin 5x cog3 5xdx

A:

Q: Find the indefinite integral ∫sec2 (x/2) tan (x/2) dx

A: Given: I=∫sec2x2tanx2dx

Q: If Z= sinh () x- show that:

A:

Q: 1 If f(x) = 8 tan¯¹(8 sin(2x)), f'(x) =

A: Differentiate

Q: sin 3xdx Evaluate: S 4+cos?3x

A:

Q: 2. Solve 3shn-sinx-2= over the interval [0,27). 2 sın'x-sinx-|:0

A: The objective is to solve the above expression.

Q: 9. Prove. cos x sin x 1 - csc x %3D sec x

A:

Q: Use a calculator to compute sinh x and cosh x for x = −3, 0, 5.

A:

Q: Approximate all solutions to tan(x)2 +4 tan(x)– 21=0 in the interval [0°,360°) X = |degrees Round…

A: We have to find

Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same time) 1.…

A: sin2x=1-cos2x and,  tanx= sin(x)/cos(x)

Q: of sin (4) sin³2 x sin 2x dx

A:

Q: 7. Show that sin (+ x) = -cosx.

A:

Q: sin(x - ) = -COS X 2

A:

Q: Find a root of  x- sin(x) - (1/2)= 0 correct to four decimal places by Secant Method

A: The given function is: x-sinx-12=0 Let, fx=x-sinx-12 Here, f0=-0.5f1=-0.3415f2=0.5907

Q: 52. Verify that f(x) sin x is an odd function and u fact to show that '3 sin x dx < 1 -2

A:

Q: find integral tan 6 x sec  4 x dx

A:

Q: 26. Show that the function has removable discontinuity at the origin sin 2x {²7, 2x 1 f(x) = if x =…

A:

Q: Lim メーvo s'in 5À sin 3X

A: Given: limx→0sin5xsin3x

Q: Find tan o if sin 0=2/3 and 0 terminates in q1

A: