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: i. An V21+3n an = 2¬" coS NT

A: We have to check whether given sequence is convergent or divergent. If convergent then find it's…

Q: cos(x + y)cos(x – y) = cos²x – sin?y %3D

A: Here we are going to use the formula cos(a+b)=cosacosb-sinasinb. For any a,b∈R.

Q: r2 cos 0 d0 /1 – sin 0

A:

Q: Sin 0/1 + co² B) 2.

A: sinθ1+cot2θ                             =sinθ1+cos2θsin2θ…

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: 2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0

A:

Q: 4.1- cos? 0 = sin 0cose tan 0

A:

Q: 5. Evaluate π/3 π/6 cos3 x sin−2 xdx.

A: 5.Solution…

Q: cos t 1-sin t sect + tant

A:

Q: 1. Calculate ln(-/2) and acos(2).

A:

Q: cos(x) = 1/2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: sin [cot(4e¬4*)]cos*[cot(4e¬4*)] dx e^x sin²(4e¬4x) Let u = cot(4e¬4x) %3D

A: Solution: Let the given integral is I=∫sin6cot4e-4xcos4cot4e-4xdxe4xsin24e-4x ......(1) Substitute…

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: What is Arg(cos ()- i sin-)) 21/3 TC 7T 37/4

A: Thanks for the question :)And your upvote will be really appreciable ;)

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

A:

Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: d²p If p = a? cos? 0+ b² sin2 0, then show that p+ a²b? %3D COS p3

A:

Q: 3. sin[cos¯(4/5) – tan-'(3/4)]

A:

Q: Find the equation for a sine function with: 32 • Amplitude = 3 • Period = • Phase shift = (-) n •…

A:

Q: 1 – - 1 + z" If z = tan show that cos a =

A: Given: z=tan α2To prove that cos α=1-z21+z2

Q: y = cosx sinx

A: Given query is to the derivative of the expression.

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

A:

Q: (a) 2(cos +i sin 플) (b) 3(cos + i sin E)

A: Solve for part (a), as follows: 2cosπ8+isinπ8=2122+2+i.122-2=2+2+i2-2=1.847759+0.765366i

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. [(3sin 2f – 3 cos 5t )dt 5. sin x dx cos x

A: 4) Given:            ∫3sin2t-3cos5tdt       =∫3sin2t dt-∫3cos5t dt taking constant out…

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: 1-sinx If y= find y'. 1+sinx

A: We can use the quotient rule to find the derivative of this function.

Q: S™ sin dt Sa" 2 1 b. 2 С. 3 d. None of the above a.

A: Given that, I=∫02πsint2dt we have to find the value of given integration.