13) sin z cos r dr

Q: snip

A:

Q: If sino + sin'0 +sin' 0 = 1, then prove that cos 0-4 cos* 0+8cos 0 = 4.

A: sin2 x + cos2 x = 1.

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

A:

Q: - 1, z = cos-

A:

Q: sin (+) can be expanded to: π TT O sin COS sin sin 4 7 TT O sin sin COS cos 4 T Osin COS + cos sin…

A: Solved below.

Q: So 3 3 cos y sin y dy

A:

Q: =/2 4. cos z dr Jo da 5. I+1 I +IA

A: We have to evaluate the indefinite integral

Q: B. If sin u = tan u < 0, find : 1. sin u/2 2. cos u/2 3. tan u/2

A: Given that, sinu=tanu&lt;0

Q: Let 3 sin z+ 6 cos y= 4.

A: The first derivative of y with respect to x is given by the expression . The second derivative of y…

Q: 3. e<4TI. 2. ind 3. where when tan e = -

A:

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: 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: 12 "2 If Y= \n(Sinae), Prove y =y=- ノ

A: Here, the given function is: y=ln(sin x) So, y'=1sin x(cos x)=tanxy''=ddx(y')=ddx(tan x)=sec2x

Q: IF Z= Cos o+isin@ prove i tan %3D 2. 1ナて

A: we use Trigonometry identities to solve this Question

Q: Prove the following identity: 1+ cos(2y) sin(2y) 1+ cos(2y) sin(2y) 1 tan(y)

A:

Q: Find the crea trom X = 0 to 2 rad y=2 sin '/2 Tr x.

A:

Q: 9 sin sin 2O° =Y 1o) cos cos 70 = a4 24 1)Sin Sin 7o = X 24 12) cos cos 20 = _ x %3D 24 24 20

A:

Q: 1) Find thesexact value o niSinG/2) ban sin x Ei Joven that 4 2.

A:

Q: Compute / sin? æ dæ. sin 2x + C 4 sin a +C 3 cos 2x + C 4 2 sin 2x + C 4 cos 2x + C 4 2

A:

Q: (b) в — р2'а, + psin'ф а, + 2pz sin' ф а, sin²o as + 2pz sin*ф а,

A: The complete solutions are given below

Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x - 4 sin°x.…

A: Evaluation of the definite Integral

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

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

Q: Let y = sin(sin(50)). Then y" is equal to: %3D Q7 -25 cos (50) sin(cos(50)) – 25 sin(50)…

A:

Q: 3 then tan 0: sin e = O 5 3. 3 O 3

A:

Q: If Z + i sin) then Z²-Z+1=.. = cos 2 b 2- -2

A:

Q: *(+²–1) cos[cosh (In r")]dr 4.

A:

Q: 3 6. Show that [[[ y sinzdxdydz = (1– cos1). 2 COS %3D 00

A: We have to prove given integral

Q: Prove thet (1+ cose -isine)" +(l+ Cos e+isine)" = 2""cos (em). %3D Co."(을) COS

A:

Q: 2. Prove: cot?x – csc²x = -1

A: To prove the given expression

Q: 1 then sin 20 is equal to 2 If 20 is in QIl and cos 30 cos 0 + sin 30 sin 0 V3 1 1

A: The given trigonometric problem is solved below in detail.

Q: 7) sin Z 32 40 Y 24 9) cos Z

A: the objective is to find the trigonometric ratios.

Q: .3 4 cos³ 4y /sin 4y dy

A: To find out the integration.

Q: 1 을 with If sin B B in Ql, find B sin ? В sin 3 + 2 6. 2 B sin 3 + 2 3+22 sin 2 6 sin 2 B 3+2/2

A:

Q: (7) (a) Prove the identity using Double Angle and Sum to Product Formulas: sin 10x cos 5x %3D sin 9x…

A:

Q: T 2 r = 2 + 4 cos 0 Option 1 r = 2 + 4 sin 0 Option 3 axis? r=2-4 sin 0 Option 2 r=2 sin 30 Option 4

A: Which of the following is not symmetric with respect to the pi/2

Q: cos x cot x COs X = 0

A: cos x cot x - cos x = 0 cos x (1-cot x) = 0 x ∈ [-π, 0)

Q: 22: Evaluate Sea s cos²(y s) ds.

A: Solution:-

Q: 7x sin 4 %3D nswer, including any

A:

Q: Q/ IF y = Sim ܠܐ 10²² (4) y = 3/² sin(x) cos(x) Prove that

A:

Q: Find z where z = sin (æ²) cos (4²) COS

A: The given function is z=sinx2 cosy2.

Q: sin(x + y) – sin(x – y) = 2 cos x sin y

A: sinx+y-sinx-y=sinx cosy+cosx siny-sinx cosy-cosx siny=sinx cosy+cosx siny-sinx cosy+cosx siny=cosx…

Q: 3. If tan(a-iß) = x- iy , show that x? + y?-2ycoth2B = -1

A:

Q: 2 COS os²(5æ) sin*(5æ)dr 4

A: This is a problem of integration. Based on the general formula of integration we will solve the…

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

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

Q: 5.3 Evaluate (sin (x)cos“(x)dx

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: dx O 32 cos 35 스) -Scos ()+7] + c O 32 cos ()- -cos+c O 32 7 32 CO 5 32 cos 35 (즐) 5sin)+21+C

A: A detailed solution is given below