Evaluate. 76) 67 1 76) sinsin 7 D 0-4 87 6л A) B) Find. 77) 77) sin (cos-1 x) D)V1-x2 1 B) 1 - x2 A) X 78) tan (cos-1 x) 78) 1-x2 A) 1 X 9 i-x2 B) DJ-x V1-x2 X Multiply and simplify 79) (cos x - sin x)2 A) cos2x + 2 sin2x 79) B) 1 - 2 sin x cos x C) 1 D) cos2x + 2 sin x - sin2x 80) cos 0 sin e (sec 6- csc e) 80) A) sin 0 - cos e B) 1 C) sin 0 - 2 csc 0 D) cos2 e- 1 81) (1 cos x) (1 + cos x) A) cos2x - 1 81) B) sin x + 2 csc X C) sin2x D) 1 +2 sin2x Simplify the expression. cos4 x-sin4 x 82) cos2 x - sin2 x 82) A) -1 B) 1 0.40 1 C) cos2 x- sin2> 1 D) -_ cos2 x - sin2 x A-30

Q: 7. tan(3 + 4i)

A:

Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

A:

Q: B- If x+= = 2 cos Ø prove that x"+ 2 cos rø by used complex number.

A:

Q: 73. Use De Moivre's theorem to show that 2( cos + isin 9. is a cube root of 8 cos 9 + isin- 3

A: De Moivre’s theorem is (cosθ+isinθ)p=cospθ+isinθ We have to prove that:…

Q: Verify the following identity. sec 0 - 1 tan 2 2 sec 0 + 1 Which of the following three statements…

A:

Q: Find all solutions of cos2x + cosx = 0. + na, 3 + na, nK, wherenis an integer + 2nn, where n is an…

A: Simplification

Q: using De-Moivre's theorem prove that cos π/7, cos 3π/7 and cos 5π/7 are the roots of 8x3-4x2-4x+1=0.…

A: The given equation 8x3-4x2-4x+1=0 Roots of the equation are cosπ7, cos3π7, cos5π7 use trigonometric…

Q: Prove that L (sin² x 2/3 ; p} = 1/ 108 р x (1²,5 + 4)

A:

Q: Let z1 = 4 (cos 7π/12+ i sin 7π/12) and z2 = 2 (cos 5π/12+ i sin 5π/12) Find z1z2. Find z1/z2

A: Recall:  z1z2=r1r2cos(A+B)+isin(A+B) z1z2=r1r2cos(A-B)+isin(A-B) We have, r1=4, r2=2, A=7π12,…

Q: 10. SHOW ALL WORK Verify the following identity:1 (1 - csc²0) (1 + tan²0 ) = tan² an evels to sty…

A: Given;  (1-csc2(theta)) (1+tan2(theta)) =tan2(theta).

Q: What is the cofunction of the complement of tan 50 o?   a. tan 50o   b. cot 40o   c. tan 40o   d.…

A: Giventan(50°)

Q: Write in standard form using de moivres theorem [2(cos25deg+isin25deg)]^6

A: Explanation of the solution is given below...using the de moivre theorem

Q: Show that (cos 0 + i sin 0)" = cos n0+ i sinne for n = 3 and n = 4.

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Prove cos 4x = 8 cos4x − 8 cos2x + 1.

A:

Q: Prove that: 1. Z, Z2 =r,r2[cos(8, + 02) + i sin(8, + 02)] 2.4=(cos(0, -62) + i sin(0, – 0,)] %3D 3.…

A: Here we use exponential form to represent complex Numbers.

Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

A:

Q: B- If x+ 2 cos0 prove that x" +2 cosro by used complex number.

A: we have to show that the following

Q: Which of the followings are false? I. General term of {2,3,2,3,...} is an =;+(-)". . General term of…

A: The details solution is given bellow.

Q: prove 2sin-1 (3/5)=tan-1(24/7)

A:

Q: Prove that (7 sin2m-10 cos2n-10 = – B(m,n)

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 5. Show that de (tan 8) can be expressed in the form 3tan 8+3sec2e-3. Hence, find tan*e de.

A:

Q: Determine whether the positive or negative square root should be selected. 1+ cos 565° cos 282.5° =…

A:

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

A:

Q: 7π/12+

A:

Q: 3. Derive and prove that cos 2x= 2cos'x-1, if the identity cos(A+ B) is given.

A:

Q: (a) Evaluate by parts: |x cos4xdx

A: In this question we have to find solution by using Integration by parts.

Q: (a) Prove that, ifn>1 is a natural number, then tan"(r) dr tan-(r) tan" (4) dr. R-1 Use this formula…

A:

Q: 3 Show that sin"0= 8 2 1 cos (20) + cos (40). 8 Which of the following four statements establishes…

A:

Q: 6. Show that (1) Cou(B1, g) = 0 (2) Cov(3o, B1) %3D

A:

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

A:

Q: Compute cos (2). As a helpful comment, notice that 4. 4 O V3+v2 || kko

A:

Q: B- If x+! += 2 cos prove that x"+= 2 cos rø by used complex number.

A: we have to show that the following

Q: Determine which statements are possible for some real number z.     cos z=2

A: The given statement is cos z=2. The range of the cosine function is -1,1.

Q: 5- Prove the following (Answer two only): secA. secB.cscA.cscB a- cos*e – sin*o =cos²0 – sin²e c- =…

A: Answer 2 only.

Q: Give the general soulution for 5cos2x-1=-cos2x+2

A:

Q: Find the points of intersection between r 2 = 2 cos20 and r =- %3D 1- cose

A: We have to find the intersection between r2=2cos2θ and r=21-cosθ.

Q: Prove that (1+i)" + 1(1- i)" = 2m/2*1 nt cos 4

A:

Q: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function:

Q: pose m and n are const (-)+(+)x] + C m-n m+n [-cos(m-nx- -cos(m-n)x - cos(m + n)x] + C 1 m+n…

A:

Q: Prove that there exists a value of r so that COS I -1 COS %3D

A: Givencosx=cos-1x

Q: Prove that there exists a value of x so that cos x = cos−1 x with full math solutions

A:

Q: Show that w = 2(cos 15° + i sin 15°) is a fourth root of z = 8 + 8iy3 by raising w to the fourth…

A:

Q: 2 Verify the identity 4cos x (20 points) 2 2 2 4sin x cos²x + 4sin²x − 4sin³x = 4cos²x.

A:

Q: the exact value of the following expression. 11 3T tan 6. 4 + tan 6. tan - - 4 E. 11T 1- tan tan - -…

A: We know that tan(a+b)=tan a+tan b1-tan a · tan b. Thus, tan11π6+3π4=tan 11π6+tan 3π41-tan 11π6 · tan…

Q: 9.2. If z1, z2 # (1/2) + kT, show that tan 21 = tan z2 if and only if 21 = 22 + kT, where k is an…

A:

Q: When r^2 = x^2 + y^2, we have x = rcos theta and y = rsin theta, and  When r^2 = y^2 + z^2, we have…

A: Consider the following: When r2=x2+y2 , then x=rcosθ  and y= rsinθ, When r2=y2+z2 , then y=rcosθ and…

Q: show that. 19 -18 O Sin 8= ē-e 2) Sin(-9) = -Sing 3) coshio = cose %3D 2.

A: Here we use the properties of trigonometric functions and hyperbolic function.

Q: 10. Prove that 7/2 sin 8 cos (cos a cosec 0) de re/2-a (1–cos a). 2

A:

Q: Find the exact value of:

A: Given that, To find the exact value of  sin 7π12 by using the identity, sin ( A + B) = sin A cos B…