14. Find dr/de: r= 0 sin 0 + cos 0 а. cos @ b. 0 cos 0 0 sin 0 C. O a O b

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

A: Establish the identity

Q: Verify the identity: cos(α - β)/(cos α cos β) = 1 + tan α tan β.

A: We will use the identity

Q: 47' sin z = x³ . cos z + sin z - 3z² Select one: True False

A: Given that d(x3 sinx)/dx  . Here we derivative of this question with respect to x. We know that…

Q: True or false: If cos A is negative, then cos (A/2) is negative as well.

A:

Q: Find the steady-state motion of the mass-spring system modeled by the ODE when t = 10 to three…

A:

Q: 2. Solve 2 sec 0 + tan 0 = 2 cos 0, 0<0<2n .

A:

Q: What is the exact value of 2sin(x/2) * cos(x/2) if sin of x = 3/5 and cos of x = 4/5 ?

A: To determine the exact value of the expression.

Q: 1. Explain why sin(n+0) =-sin@ using a diagram and x, y, and r.

A: Solution of given problem is followed by

Q: Eliminate 0 from the equations : (i) x = h + a cos 0, y = k + b sin 0 (ii) x = a ser³ 0, y = b cot³…

A: Solution is given: Hope the solution is helpful.

Q: 38. Differentiate y = 2 cos² - a. – sint b. - sin 2t C. - sin - d. sin-

A: Differentiate y=2cos2t2

Q: Q2/ A) Prove the identity Sin (A + B) + Sin (A - B) = 2SinA cosB %3D

A:

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

A: We will use the Differentiation under Integral sign method, to solve the problem.

Q: sin(0) = - 2 V3 csc 0 = 2. cos 0 = -. Cos O sin 0 cos 0 = 0.

A: Please refer the attached image for complete solution. THANK YOU.

Q: 1. Suppose we know sin a = and 0 < a < , and suppose we also know cos 3 = 2√³ and - < 3 < 0. Use…

A: Given: sinα=35, 0&lt;α&lt;π2 and  cosβ=255, -π2&lt;β&lt;0 To find:  d) sin2αe) cos2βf) cosα2

Q: 10. Prove that 7/2 sin 0 cos ! (cos a cosec 0) d0 /2- TC (1-cos a). COS

A:

Q: 6. Prove that: ah cos (i) A sin (ar + b) = 2 sin (ah sin a (ii) A cos (ar + b) = - 2 sin

A:

Q: s 4

A: To simplify (cos 3x)(cos x)-(sin 3x)(sin x)

Q: Determine the value of  tanz if sinz + cos z=0.2 and pi>z<pi/2

A:

Q: Verify the identity : cos(α - β)/(cos α .sin β) = tan α + cot β

A: Given : cosα - βcosα sinβ = tanα + cotβ

Q: 7. Determine all the solutions to the equation in the interval [0, 27): sin 20 cos0 – cos 20 sin0 +1…

A: As we know that Sinx-y=SinxCosy-CosxSinyThe genaral solution of Sinz=-1  then z=Sin-1-1=nπ±π2

Q: Cos z+1 cos 2 1 + sec x =

A: Use simple trigonometry relation.

Q: 16. Establish the identity: os 0)² + (sin 0- cos 0)2 = 2 %3D

A: We need to establish the identity  (sinθ+cosθ)2+(sinθ-cosθ)2=2

Q: Verify the identity sin t - cos 2t = (2 sin t - 1)(sin t + 1).

A: sin t - cos 2t=(2sin t-1)(sin t +1)Formulascos 2t= 1-2sin2t

Q: If cos a + cos B= a and sina + sin B= b, then show that 2 sin 2a + sin 2B = 2ab 1 a2 + b2

A: given: cosα+cosβ=asinα+sinβ=b we have to show that  sin2α+sin2β=2ab1-2a2+b2 R.H.S: 2ab1-2a2+b2…

Q: 2) Find the value of: sec(tan )+ cos(sin ? 2. CoS

A:

Q: Find cos x + sin 2x dx 19. sin x

A:

Q: 4. Solve 2 cos²x - cos x = 1, x = [0, 2π] for the exact values of x in radians or two decimal places…

A:

Q: উদাহরণ-9. যদি tan c হয় তবে প্রমাণ কর যে %3D - a

A: You need to find the values of sine and cosine of from the given value in the question.

Q: 4. sin 2x cos 2x dx

A: Here we integrate the given function.