13. (a) cos (b) sec 3 (c) sin (-) (1) ese(-) 14. (a) tan (c) cot 15. (а) сos 6. (b) csc (c) tan 6. 16. (a) sin (b) sec (c) cot 6. to to

Q: arcsin(4x)/arctan(5x)...

A: Using L'Hospital's rule to evaluate this limit,we know that,if  is of the intermediate form or…

Q: Find the value →21. csc (sec- 2) + cos (tan¬1 (– V3))

A:

Q: 6. If f(r, y) = tan-(x/y), then the value of f,(3, 2) is %3D -3 (b) (c) 1 (d) -2 (a) 13

A:

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: D cos( 5t D sinf see Dcost cast) 4

A: See the attachment

Q: If u(s) = -11 ((s)°) (cos(s)), then: а) u' (s) = 11s (s)') sin(s) – 55s(s)*(cos(s)) – 11 ((s)°)…

A:

Q: Ja + + tan x) sec?x dx

A:

Q: 2) Show that: cos (0) sin (0) (6) (5) - (² Xp = Yp sin cos (0) a))) ||rp|| cos (0 - a) -||rp|| sin…

A: This answer is given below.Explanation:

Q: S COS X sin x+sin³ x dx. (b) ſ sec²x tan x+4tan³ x dx.

A:

Q: 2" cos(r) dr.

A:

Q: Evaluate tan" (32) sec"(3e) dz. sec" (Зa) da.

A: Here we integrate using substitution method.

Q: dr os(-³/)| = ( In cos

A:

Q: 1+ csc x cos x + cotx

A: Given query is to simplify the expression.

Q: Find f), (b) f(r) tan(2r)

A: To find f’(x).

Q: T/4 (b) 4 sec (0) tan(0)dө.

A: Answer is- 4(√2-1) Explanation is given below...

Q: e² tan (e²) b) dr I sec2 (e-) – 7

A:

Q: e* tan (e*) dx sec2 (e*) – 7

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: b) if J(zf64)} - 39ga) ) ce = Sin () %3D and S(3f (x)+9 6)) dx = tan () 2. 2. +596)) dx

A:

Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: Lim メートo Cos aX Cos bX

A:

Q: -7) 6 (b) csc (-7) (c) tan(–7 6 (a) cos

A:

Q: Differentiate y = 5 sin(2x-4). O a) dx = = -5 sin(2x-4) о O b) ad ax O c) = 5 cos(2x-4) = -10 sin(2x…

A:

Q: cot(sec(x) -1 cot\sec

A: on  simplifying we get

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: Cos (tan (-1)) nin (con (-4))

A:

Q: If sinh(æ) = -4 , then coth(x) = (A) (B) =VI7 (C) =VE V15 (D) 4 15 (E) E O (A) O (B) o (c) O (D) O…

A: Solution