Let k and n be positive integers. Prove each of the following:a) π−πsin2(nx) dx = π−πcos2(nx) dx = π.b) π−πsin(kx) cos(nx) dx = 0.c) π−πsin(kx) sin(nx) dx = π−πcos(mx) cos(nx) dx = 0 ifm = n. (25) Let k and n be positive integers. Prove each of the following:a)sin* (n.x) dz = |cos (nx) dz = 7.b)sin(kr) cos(nr) dr = 0.%3Dc)sin(kr) sin(nz) dr =/ cos(ma) cos(na) dr = 0 ifm + n.

Answered: Image /qna-images/answer/7696c652-a2c5-4e4a-b21b-3fe4c36b755f.jpg

Answered: (25) Let k and n be positive integers.…

(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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 38E

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Question

Let k and n be positive integers. Prove each of the following:
a) π
−π
sin2(nx) dx =
π
−π
cos2(nx) dx = π.
b) π
−π
sin(kx) cos(nx) dx = 0.
c) π
−π
sin(kx) sin(nx) dx =
π
−π
cos(mx) cos(nx) dx = 0 if
m = n.