cos2t dt Evaluate the Integral (1+ sin2t) 4 A (1+ sin2t) 3+ C (1+sin2t) -3+ C 6. (1-sin2r) 3+ C 6. D (1-sin2r) -3+ C

Q: Evaluate the integral: f cos³x cos 3x dx

A:

Q: sin(2u) cos(2u) sec u c) sin u c u

A: We have to show that sin2usinu-cos2ucosu=secu We have to consider the left hand side of given…

Q: (b) D₂f = 2 cos(xy + 2z) Dzzf = -4 sin(xy + 2z) Dzzyf = -4x cos(xy + 2z)

A:

Q: 3 п (3 2 sin (x-2п) cos ( -x ) + tan (п -x) tan 3 п 2 +x

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: 13x (b) sin 12

A: NOTE: Refresh your page if you can't see any equations. . use the formula

Q: 5. Prove: tan²xsin²x = tan²x – sin²x

A:

Q: T/3 3 sin (3t) -dt. 5 - cos (3t) Evaluate the integral

A:

Q: 8. If sinx = , x is in quadrant II, then the value of cos2x is %3D 17 b) -161 30 161 353 a) 289 c)…

A: Given : sin x = 817 x is in quadrant II.     To find the value of cos 2x.

Q: Prove that 1 3V2 dx < 3 + x (Hint: Theorem 5.9(ii) and carefully chosen functions should do the…

A:

Q: Determine the amplitude of the sinusoidal function - 4 sin 3(x - ) +2 y = Your answer

A:

Q: tan-¹ (sin) 0 - 4 O Оп 0-1/2

A: we know  that  sin(π2)=1let  y=tan-1(sinπ2)

Q: D cosh x dy + Cy Stnhx +e) dx - o +ě) dx =

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: ſcos^4 (2t) dt * O 3/2 t + 1/2 sin4t + 1/16 sin8t + C O 1/4 (3/2 t + 1/2 sin4t + 1/16 sin8t )+ C O…

A:

Q: A B 25/sin² 5 (sec 0 - cos 0) d )* Which of the following is equal to S; x² +25 dx ?

A: The given integral is x2/sqrt(x2+25).

Q: d 1+ sin² (2)| dz

A:

Q: 6) 1-cosx %3D 1+cosx (cotx - cscx)2

A:

Q: - 4x + 30 -dæ Evaluate (x – 5)(x + 5) + C

A: To solve the given integral first break the integrand into the simple expression using partial…

Q: dx 1+x2 A In(1+x²) + c BIn(1+ x²) + c c tan-ix +c 1 x 2 D tan-x+ c IN

A:

Q: Evaluate D 6 |3x|√9x²-4 3 2 sin-¹3-sin-¹ 3 tan¯¹3-tan -1 1²/24 sec ¹3-sec dx sec-1³/12

A:

Q: 3. ſsec? x(1+ tan x)/tan x – 1 dx ans : 3 (tan x – 1)' + ¿(tan x – 1) +c 4. S'cos x(2+ sin x)/2 +…

A: 3. Given integral is ∫sec2x(1+tanx)tanx-13dx Substitute tanx-1=z⇒tanx=z+1sec2xdx=dz Therefore, the…

Q: Exercise(6) Prove that J1/2 = XT sinx 2.

A: Here we have to prove that  J12=2xπsinx

Q: Multily    (a) (a+b)  2 (cos theta - sin theta ) 2

A:

Q: Integrate 0 1 S √1 1-4x2 dx using a trigonometric substitution. sin-¹ (2x)√1-42²+ C 0 1 -sin-¹ (2x)…

A: The given integral is sqrt(1-4x2).

Q: XV3X-4 V3x-4 +C tan 3x-4 +C sin' 2 tan 3x-4 +C sin 3x-4+ C None V3x=4 tan +C 2

A:

Q: 1+cos 4x dx 1-cos 4x Evaluate

A:

Q: f(csca cot a + ba*)da csc * +x6 +e cot & + x + e 6 CSC * - +c CSC * +z6 - csc * +a +e .6 CSC * – *°…

A:

Q: r = 2 cos(4 e) r= 1+1 sin(0) r = 3 cos(2 0) r = 1+ 4 sin(e) r = 3 sin(3 0) r = 3 - 2sin(0) %3!

A: To match the given figures with the given equations.

Q: Sin 3 o0Tt sin (5 sin 2nt) + Sin z00 Tit sin(ssinzr t)

A: Assume to simplify the given expression. sin300πtsin5sin2πt+sin300πtsin5sin2πt=2sin300πtsin5sin2πt

Q: True or false? sin45∘cos30∘−cos45∘sin30∘=sin60∘cos45∘

A:

Q: tany-tan 2 π 1+ tany tan 2

A: Note that tanπ2→∞. Thus, the expression tany-tanπ21+tany·tanπ2 is not defined.

Q: 3) (sinx + cos x)² = sin 2x + 1 COS %3D

A: We have to prove that  (Sinx+cosx)^2=sin(2x)+1

Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

A:

Q: Part 1 of 3 35 3 << 37 2

A: Given that the expression

Q: 1+sin-1t Find A' (t) if A(t) 1-cos-1t

A: Given: At=1+sin-1 t1-cos-1 t To Find:  A't=?

Q: Sz sin?m-10 cos2n-10 = – B(m,n) В (т,п)

A: