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f) Show rigorously that if f(x) = cos x then f'(x) = sinx. You can use without proof that lim sin a = 1. x-0 X how to get this? f) Several solutions are possible. Trigonometric identities: cos(x + h) cos(x) = -2 sin(x + h/2) sin(h/2) Hence sin(x+h/2) sin(h/2) = lim h→0 - cos(x + h) cos(x) h - = -2 lim h→0 sin(h/2) h→0 h/2 lim sin(x + h/2) lim h→0 - sin(x). h

f) Show rigorously that if f(x) = cos x then f'(x) = sinx. You can use without proof that lim sin a = 1. x-0 X how to get this? f) Several solutions are possible. Trigonometric identities: cos(x + h) cos(x) = -2 sin(x + h/2) sin(h/2) Hence sin(x+h/2) sin(h/2) = lim h→0 - cos(x + h) cos(x) h - = -2 lim h→0 sin(h/2) h→0 h/2 lim sin(x + h/2) lim h→0 - sin(x). h

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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[Trigonometric identity] Could u please tell me how to convert the LHS to the RHS using trigonometric identities? Thanks :)

f) Show rigorously that if f(x) = cos x then f'(x) = − sin x. You can use without proof that lim sinx = 1. X x →0 this ? how to get f) Several solutions are possible. Trigonometric identities: cos(x + h) — cos(x) = −2 sin(x + h/2) sin(h/2) Hence || lim h→0 cos(x + h) cos(x) h - lim sin(x + h/2) lim h→0 -2 lim h→0 sin(h/2) h→0 h/2 sin(x + h/2) sin(h/2) h = – sin(x).
Transcribed Image Text:f) Show rigorously that if f(x) = cos x then f'(x) = − sin x. You can use without proof that lim sinx = 1. X x →0 this ? how to get f) Several solutions are possible. Trigonometric identities: cos(x + h) — cos(x) = −2 sin(x + h/2) sin(h/2) Hence || lim h→0 cos(x + h) cos(x) h - lim sin(x + h/2) lim h→0 -2 lim h→0 sin(h/2) h→0 h/2 sin(x + h/2) sin(h/2) h = – sin(x).
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