Q.3) Prove that L-1 ) =(coshat sinat + sinhat cosat) %3D 2a +4a

Q: 5. (tan2x + cot2x)² dx

A:

Q: Show that sin-1 v + cos-1 v = π/2 .

A: Given: sin-1 v+cos-1 v=π2

Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: (a-B) show that cosa – cosß = -2sin+P) sin 2 2.

A: We have to show that the following results.  For this we can use some trigonometric results

Q: Sine coixdx 5/2

A: We need to integrate∫sin52xcos2x dx

Q: 2. [e1/² cos 2tdt Set/2

A:

Q: Prove : (1 - cos E)(1 + cos €)(1 + cot²0) = 1 %3D

A:

Q: Find the arclength of fox) = Ln/sinx/ on [1, 2] Round the answer to 2 decimals.

A:

Q: Cosx 1+sinx 11. 1+sinx 2secx Cosx

A:

Q: (arctan o tan)' = 1 – pi k E z°(k +1/2)pi When differentiating on the Real line is this true?

A:

Q: e' [ S (5² +a²) 2 ] = t sinat 2a 7 Prove using Convolution

A:

Q: f (x) = 7X 0< RくL 1<スc2

A:

Q: O Find the anfidanialtiner Sfaw da for fla)= 18 Cos (6x) 16- Sin? (6x) © fa) = ¿* (, +x) 9 + xe

A:

Q: und tre e given t Coslutl

A: To find the exact value of cos(u+v)=cos u cos v -sin u sin v and we are given that  sin u =-35 ; cos…

Q: (sece +tane)(1+sine)de =

A: Evaluate ∫π6π4secθ+tanθ1+sinθdθ

Q: lim ze = -9 cos 3 + i9 sin 3. %3D Select one: O True O False

A: The statement is TRUE  The detailed solution is as follows below:

Q: Q6) Calculate the mean value of y= 24 sin5 0 cos 0 from 0 = 0 to 0= J\6

A: Mean value is evaluated.

Q: Q2-By using the formula cos(A – B) = cosAcosB + sinAsinB & %3D sin(A – B) = sinAcosB- cosAsinB…

A:

Q: a) Prave that sinlx t Cos-lx = ½ %3D

A: To prove,   sin-1x+cos-1x=π2

Q: 2. Prove that, V{(sec 0 - 1)/(sec 0 + 1)} cot 0. = cosec e

A: