Prove that ; cosec x . cosec 2x . sin 4x . cos 6x . cosec 10x cos 3x + cos 5x cos 7x cos 9x sin 2x sin 4x sin 4x sin 6x sin 6x sin 8x sin 8x sin 10x

Q: 2) DISCUSS The Contmuyo f Sin TX %3D

A:

Q: that "C₁ sin 2x + "C₂ sin 4x + "C3 sin 6x 1+ "C₁ cos2x+ "C₂ cos 4x + "C3 cos E x; where ne N

A:

Q: 5. Prove: tan²xsin²x = tan²x – sin²x

A:

Q: Evaluate cos x + 2 cos x +1 dx sin' x sin x 主x+c sin 主tC 3 sin x cos x COS X + x +c cos xsin X 3 COs…

A:

Q: "(등 -2) + ain (품 + 22) The simplified form of cos 22x) + sin O V3 cos 22x + sin 22x O v2 cos 22x + 2…

A:

Q: Express as a product. sin 4ẞ + sin 10ẞ + sin 22ẞ + sin 16ẞ

A:

Q: (종-272 27=) + ain G + 272) The simplified form of cos O V3 cos 27z + sin 27z V3 cos 27z + v2 sin 27z…

A: Given cosπ6-27x+sin(π3+27x)

Q: Verify the identity. (sec ² 0+1) (- sin² 0+1) = 2-sin ²0 20 rch Which of the following four…

A:

Q: Verify the identity. 2 cos 2x sin 2x = 2 csex 6 sinx sinx COSX Continue Statement 2 cos 2x sin 2x…

A:

Q: Stan 2xdx O-In(cos 2x) + C O-In (cos 2x) + C O-In (sin 2x) + C O tan² 2x 2 + C

A: INTEGRATION

Q: | 13 csc (5z) cot(5z) dz =_ (Use Substitution Method) o 13 13 +C 10 sin (5z) 10 O 13 13 10 10 sin…

A:

Q: (b) Show that: cos(x cos 0) = Jo - 2J₂ cos 20 +2J4 cos 40 +

A: Solution (b):

Q: 25-11 2-4s + 8

A:

Q: Evaluate V1-289z2 sin (16x) + C 17 1 sin 1 (17x) +C 17 sin (16x) + C 17 1. sin (17x) + C 17

A:

Q: The simplified form of cos ( - 5z) 5z) + sin 6 52) + sin (; + 52) O v3 cos 5x + v2 sin 5x O v2 cos…

A: This can be evaluated as:

Q: sin5 4 3 cos6 4 4. dw

A: Giventhat:-∫π3π sin5 34ω cos6 34ω dωTo find:- value of IntegralSolution:- Integral ∫sin534ωcos6 34ω…

Q: Verify the identity. cos 7x- cos 9x tan 8x sin 7x- sin 9x Statomont

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Q: d da cos(3) = O-3 sin (3²) O 32.cos(3²) -3.sin(3²).In 3. O sin (3²) O3 cos(32).In 3

A: Given

Q: Show that n. In(cos 2k+2) = - In (2"+ sin 2n+2). k=0 Hint: sin 20 = 2 sin 0 cos 0.

A:

Q: Cos ax COs ax Q: Prove that dx = ze", a 2 0.(or) Evaluate x² +1 x² +1

A:

Q: Use substitution to evaluate the integral 4 sec2 4xvtan 4xdx 4 (tan 4x) + C 3 15 (tan 4x) + C 2 (tan…

A: Given query is find the value of the integral.

Q: | sin2xdx = %3D cos2x A O +C cos2x B O +C 2 cos2x+CCO -2 cos2x+CDO

A: ∫sin(2x)dx= -(cos2x)/2+C

Q: Express as a sum.(sin ax)(cos bx)

A: Given : (sin ax)(cos bx)

Q: ze pu хе and Ze ле of ye"- 5 sin 32 32

A: Given query is to find indicated derivative.

Q: (b) cos cos ( 13 ) 131 18 21 18 21 sin COS -sin 18 18

A: To evaluate the given trigonometric expression

Q: Evaluate: fcos In(sin 0 + 4) de O sin In (sin 0 + 4) - 2 cos 0 + 3 ln sin 0 + 4] + C O None of these…

A: