4. Describe a way of evaluating x cos? x dx. sin' х. х со

Q: 4. Establish the identity: sec ar - secr sin2 = cos LIC HS O6Y

A: Establish the identity

Q: - 1, z = cos-

A:

Q: Verify that if y = ƒ(θ2 sin θ, then y'(θ) = ƒ'(θ) sin θ + ƒ(θ) cos θ.

A: We use the product rule

Q: Evaluate : 1) | cos x 3) [ cos x 2) [ ,cot ydy sin' x 1+ sin x 7/4

A:

Q: Evaluate S(cos4 x – sin* x)dx

A:

Q: s nip

A: Given z=tanα2

Q: 2) VERIFY THE IDENTITY sin +0 =-cos 0. 2.

A: We need to verify the identity.

Q: Differentiate implicitly cos(x³y³) = 9

A: Given,         cosx3y3=9

Q: If sin u  = 3/ 5 and sin v = 4/5  and that u and v  are  between  0 and π/2,   evaluate :     cos (…

A: given: sinu=35 sinv=45 and u and v are between 0 and π2. we have to evaluate cos(u-v)

Q: 4. Verify the identity sin(z+y) %3D COB E COS y tan z+ tan y

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: 9 If f(0) = cos 01 cos 02· cos 03 ... cos On + tan 0,}=- f (0) Show, {tan 0, + tan 02 + tan 03 +…

A:

Q: S sin° (3t) cos(3t)dt Evaluate COS

A: To determine the value of the integral.

Q: 1. If z = sin2+In^, find the value of x- +y X

A:

Q: 2. What is the exact value of cos()? |(0, 1) (글,

A: Graph is symmetrical in -2 to 2. So the midline of function is y=0.

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

A:

Q: 8. Show that cos a – cos y| < |x – y| for all æ and y.

A:

Q: A = -, find sin 2. If 90° <0 < 180° and cos 0 :

A:

Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

A:

Q: 3. Evaluate 5 sin rdr

A:

Q: 4. Evaluate et cos xdx.

A:

Q: Compute : exp(i sin(e-i))

A:

Q: Prove the identity. cosx sin (x+y) – sinx cos (x+y)= siny

A: In question We have given two identities and we'll prove it, (i). Cos(π + x) = - Cosx  (ii). Cosx…

Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

A:

Q: Prove 3n - T, 2 sin? x – sinx cosx – 2 cos? x=0 in has five root's Hint. Intermediate value theorem

A: Corollary of Intermediate value theorem :- If a continuous function has values of opposite sign…

Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: Evaluate S (cos4 x – sin“ x) dx

A:

Q: Calculate ∫9sin^4(x)cos^2(x)dx

A: Given: ∫ 9 sin4 x cos2 x dxFormula: cos2 x = 1-sin2 x…

Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

A:

Q: Prove the below cos' x sin 3x + sin' x cos 3x 3 sin 4x 4 II

A: Simplification of trigonometry function

Q: Find x so that sin 3x + 10 cos x+ %3D

A: Here we have to find the value of x. The solution is following.

Q: 2 , 1 + sinx +. D. cosx cosx il + sin.x

A:

Q: 4 Find sin 2x, cos 2x, and tan 2x if cosx= and x terminates in guadrant III.

A:

Q: 13T (b) sin-(sin(- -)) = %3D 11

A:

Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

A:

Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: 5) prove that = sin 'x +e using method of trigonometric substitution.

A: To Prove- Prove that ∫dx1 - x2 = sin-1x + c using method of trigonometric substitution.

Q: 12. sin 2t – tan t = tant cos 2t - HINT: You will use a reciprocal identity.

A: use the formula

Q: Prove that 55 sin x² dx - 5 cos x² dx = 1/2 √

A:

Q: e). Prove that Sin3A+sinA 25in2A -COSA

A:

Q: 14) Show that Cos e= 1- Sino COs o : |-Sinie

A: Given, cos2θ = 1-sin2θ We have to show that.

Q: Evaluate 1) S sin ³x cos³x dx

A: Given: ∫sin3(x)cos3(x) dx

Q: Show that, for real values of x, 3 sin x f(x) 2 + cos x cannot have a value greater than 3 or a…

A: To show that the minimum and maximum value of the function is -√3 and √3

Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant IV. sin 2x %3D cos 2x %3D tan…

A:

Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: Show that 4 sin x cos 2x + 3 = 8 cos %3D x.

A: We will use the formula of cos 2x and other formulas of trigonometry to prove left hand side is…

Q: In sine sin -1x os (sin-!x) + C cos V1-x? 1-x² A) True В False

A: To check:  ∫sin(elnsin-1x)dx1-x2=-cos(sin-1x)+C is true or false.