3 4) Sain ³x cus³x dx 3 a) - + cos²³x (vin³x + ²) + C 2 b) = cos²x (Ain²³x + ²/2 ) + Cc c) - — cos ³x (ain ²³x - ²) + c d) none of the above

Q: (1+x)(1+ry Q14) 2x (1+x) dx - A) +C B 11 10 11 10 Q15) f f(x)=x+cosx, xe [0, ], then the function…

A: Note:- As per your demand we solve question 14 and 15 for you  Given problems:-

Q: 14. Prove that (1- cos x) csc x = 1

A:

Q: 3) 3 sin x + 5 sec x tan x COS X √³5 dx

A: V=∫3sinx+5secxtanxcosxdxtanx=sinxcosxsecx=1cosx∫1xdx=lnx

Q: 13) 3 sin x +5 sec x tan x cos x dx

A:

Q: 3) Show that 1 + cot Pe=csc²e. CSC

A:

Q: 3- If xy=cotxy, and x=u" u+1 Cosu +4 find , 허 du

A:

Q: Q14) [2x (1+x²) x-(1-x²) (1+x²) +CB)- 10 (1+x¹) (1+x²) (1+x²)" (1+x²)" 11 +00) +CD) 11 10 12 1.1…

A:

Q: Show that cos 2x-cos 6x sin 6x-sin 2x b) Hence or otherwise, solve = tan 4x cos 4x cos 2x-cos 4x cos…

A: Hence proved

Q: 2) Show that: cos (0) sin (0) – sin B (6)) (*) = ( cos( 2 ||7p|| cos (0 - a) -|||| sin (0-a), -as))

A: PROOF IS MENTIONED CLEARLY IN THE EXPLANATION BOX.Explanation:

Q: 5. y + 4y = sin x + 3 cos x Ans: y = C₁ + C₂ cos 2x + C3 sin 2x + sinx-cosx

A:

Q: sin n 3 4TC

A: The given trigonometric function sin4π3 Since sinπ+θ=sinθ

Q: 3) 3 sin x + 5 sec x tan x COS X dx

A:

Q: * 37 015) 15/(x)=x+cosx, xe[0, z], then the function has an inflection point at x A)- 110) C D) # 2…

A: Asked questions are solved.

Q: b) 2 cos² x + 3 cosx+1 = 0

A: Step 1:   Step 2: Step 3: Step 4:

Q: 7 b) Prove the identity 2 cosxt sinco (1 + COS X) =1

A:

Q: 022) Find the range for the function f(x)=2+3√4-x A(-0,2] Cos r 023) lim- A) DI 2x-z C) 0 TIN Di 1

A: