(25) Let k and n be positive integers. Prove each of the following: sin (n2) dz = | cos (nx) dz = 7. b) | sin(kr) cos(nr) dr = 0. e) L. sin(kr) sin(nr) dr = | cos(ma) cos(nr) dr = 0 if m + n.

Q: Which of the following is equivalent to | cos(4a)sin (4x) da ? cos udu · 1 sin udu, where u = 4x…

A: The answer is found in step-2.

Q: By expressing the product as a sum, 2cos(3x)cos(4x)= ?

A:

Q: c. sin"(t)- cos (t) = 2sin (t)-1 = CS d. cot (2y)+cos?(2y)+ sin (2y) = csc²(2y)

A: Given,  c. sin4(t)-cos4(t)=2sin2(t)-1d. cot2(2y)+cos2(2y)+sin2(2y)=csc2(2y)

Q: 5. Evaluate π/3 π/6 cos3 x sin−2 xdx.

A: 5.Solution…

Q: a dx = 1+ sin(ax) Select one: a. tan(ax) – sec(az) + C b. ax + In | csc(az) – cot(az)| + C c. In |1+…

A:

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

A:

Q: Calculate ㅠ 2 6³ cos² (4x) sin² (4x) dx

A:

Q: One approach to evaluating 2 cos (2x)dx is to first rewrite it as cos(4x) + 1 dx а. cos(2x) – 1 dx…

A: This is the question of integration.

Q: Find Desin (cos(tan(x³ + 1)))

A: u.v rule for differentiation, d(u.v) = u.d(v)+v.d(u)

Q: sin(2t). Find Əz Ət if z = √r² + s², r = cos(2t) and s =

A:

Q: Compute 4 sin(TTX) d dx A. 4 sin(TTX) B. 4sin(TTX) In4 C. 4sin(x) (πIn4).cos(TTX) D. 4 sin(TTX)…

A:

Q: ) Find | sin can) cas (ga)da cos (gx) dx

A:

Q: You are given that h (x) C = dh dx for a number c. You have to find c. = 6 sin (7x) + 5 cos(7x) 3…

A:

Q: b) S x² cos(2 x³)dx

A: