Unformatted text preview: cos( x + y ) = cos( x ) cos( y )-sin( x ) sin( y ) sin( x + y ) = sin( x ) cos( y ) + cos( x ) sin( y ) Using these formulas, prove by induction that for any natural number n and any real number x (cos( x ) + i sin( x )) n = cos( nx ) + i sin( nx ) where i is the imaginary unit , i.e. the square root of -1 (in other words i 2 =-1). Do not convert this problem to exponential notation and try to solve it in that form. It doesn’t make things simpler and it will confuse us when we grade. Hint: this is not as bad as it looks. If your equations seem very complicated and won’t simplify, look for a mistake in your algebra. 1...
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- Spring '10
- Cos, 2k, standard trigonometric identities, Theory of Computatoin