TT True or False tan 0 • cos 0 sin 0 for any 0 # (2k + 1) %3D

Q: 1 sec A-tan Asin A = %3D sec A

A:

Q: 14. Find the smallest positive root of tan x+2 tanh x = 0.

A: Newton Raphson Method:- The root is xi+1 =xi - fxif'xi; i=0, 1, 2, ....   Given equation is tanx +2…

Q: sin 0 + In + 22+3 = -3 - cos 20 - In y? + 327-4 = + 2ln y+ 22 -3 1+ (cot 0)2

A: Given system is sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: Find the root of 1+ tanh x - 2 tan x = 0.

A: We find the root of  1+tanh(x)-2tan(x)=0 , by Newton's method.

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

A:

Q: 4. cos*x Evaluate: sin' x( sin' 3/5 x+ cos³ x 3.

A:

Q: Verify the identity:

A: Our Aim is to verify the identity given below:-sin 3π2-x=-cos (x)  -(i)

Q: CianXtl) 2 tan x 8. Prove the identity: sin 2x = 1+ tan x L.S. es

A:

Q: (a) Find S(tan x)dx (b) Evaluate i sin 3x cos 3x dx d (c) Find (2x sin 2x + cos 2x) and hence…

A: a) ∫tan2πx dxb) ∫π9π6sin3x cos3x dxc) ddx2xsin2x+cos2x and ∫0π4x cos2xdx

Q: a) Show that sin¯'x + cosx = 2 E) - tan-' (). x(x-y) y(x+y) (b) Find the value of tan1 where >-1…

A: We can solve these two question by using the properties of inverse trigonometric function as below.

Q: (a) i) Prove that 1 sin20 1 tane 1+ sin20 1+ tane for 0<0 <- 4 ii) Hence, show that the exact value…

A:

Q: (cos 0 -sin 0) d0 7. J sin 0 8. J (1 – tan 0)² de. 9. sec2 0 tan² 0 d0.

A: 7. Given integral, ∫cos θ-sin θsin θdθ

Q: Evaluate the integrals in Exercises

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Osl 2. 2Sin x- CosX+1 = 3 tan x 2 Cos?x

A:

Q: True or false: If tan 3x = any integer n. + nn for 4 1, then x = %3D

A:

Q: Evaluate (cos x In sin x) dx. Select the correct response: O cos x (In sin x-1) +C sin x (In cos…

A:

Q: – 1) sin a cos a - sin æ 9(cos² e – 1) O 9 tanx + 9 sec a O 9 cot a + 9 cscx O 9 tana + 9 csc a O 9…

A:

Q: sin ( 27 +1)x Prove that dx =7 for all ne N. Sin x

A:

Q: 9. cos (21) di 10. 11. sin'x cos's de 12.

A:

Q: 269. Please find all 0 ≤ 0 ≤ 2π, for which ... (a) tan () = √3 (b) 3 sin² (0) + 4 = 5 (c) 2…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: (2k + 1). True or False tan 0. cos 0 = sin 0 for any 0 + %3D

A: Given :            tan θ . cos θ = sin θ for any θ ≠ (2k + 1)π2.  To state true or fase.

Q: 2 2 sin a dx 1 + cos x O In(2) In(2) O In(4) In(4) -

A:

Q: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

Q: sin(x) is The solution for lim 1- cos(x) O 1 O DNE

A:

Q: 4. Prove the identity csc 0 – sin 0 = cot 0 cos 0.

A:

Q: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

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

A: y=tanu Differentiating with respect to u, we get dydu=sec2u Now clearly, sec2u≥0 for every value of…

Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

Q: 4.) Prove: sin 2x a) 2cos? x = tan x b) sin 3x = 3 sin x – 4sin3 x [Hint: sin 3x = sin(2x + x)] -

A:

Q: f/² () sin cos (sin (²) dx (Consider initially the first 2 terms)

A: To evaluate: ∫0π2sinx3cos4x3sin2x3dx Let I = ∫0π2sinx3cos4x3sin2x3dx We know that  sinxcosy =…

Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: sin 0 + In + 22+3 = -3 1- cos 20 In y? + 322 - 4 = + 2ln y + 22 =-3 1+ (cot 0)2

A: Given system is  sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: cos e sin 0 for some real value of 0, and let B= -1 Let A = Consider x - sin 0 cos 0 Then ||(AB)x||…

A: Given,            A=cosθsinθ-sinθcosθ , B=0-1-10 , x=12To find : ABx

Q: 2 sin'x - cos x sin'x - (1 - sin'x) in*s) Rule ? %3D sin°x - 1 + sin´x Rule ? %3D = 2 sinx - 1 Rule…

A:

Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: 5 sin 0 – 4 cos 0 e of 5 sin 0 + 4 cos 0 is

A:

Q: Derive a formula for ſ tan x sec "x dx where n 40

A: Integration problem....

Q: sin 0(3sin? 0+ 4cos? 0) = 3 cos 0 + cos³ 0 4. Prove that tan 0

A:

Q: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

Q: 5. sin 2 x=cos X

A:

Q: Prove the identity. 3 sin(x – y) cos y cos x 3 tan x - 3 tan y

A: Given that  3tanx-3tany=3sin(x-y)cosycosx We need to verify the given identity.

Q: 1. Evaluate 2. Evaluate sin(20) 30 x-2x cos x sin x limo lim, 0

A: Given is  limθ→0sin(2θ)3θ. L'Hospital rule: limx→af(x)g(x)=limx→af'(x)g'(x) NOTE: According to the…

Q: Cos O tan 0 66. lim 0→0

A: Consider the given function. limθ→0   cosθtanθθ

Q: 50 a) Sin 25 b) Sin- Sinl0 =? Cosl0° Sin 5° = x, Cos 5° =y Sin 105° - ?

A:

Q: x) - 0.5 cos(x)) on the

A: Given as, f(x)=e-x3.2sinx-0.5cosx in the interval [3, 4].

Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

A:

Q: |(1+ sin x)'cos x in x) cos x cOS.

A: Given: ∫1+sinx3cosxdx

Q: cos(sin (0.4252)) : O 1.9051 O 0.9051 O -0.0949 O -1.0949 O 2.9051

A: sin^-1(0.4252)=0.43918284434 that is cos(0.43918284434) =0.90509941995