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
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
[Trigonometric identity] Could u please tell me how to convert the LHS to the RHS using trigonometric identities? Thanks :)
Equations that give the relation between different trigonometric functions and are true for any value of the variable for the domain. There are six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
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