Using your knowledge of complex numbers, such as De Moivre's and Euler's formulae, verify the trigonometric identities for the double angle.
de Moivre's: (cos(x)+isin(x))n=cos(nx)+isin(nx) set n=2 (cos(x)+isin(x))2=cos2(x)+2isin(x)cos(x)-sin2(x), which, according to de Moivre's cos2(x)+2isin(x)cos(x)-sin2(x)=cos(2x)+isin(2x) We notice that on both the RHS and LHS we have real and complex terms, which means that the real part on one side is equal to the real part of the other, and the same stands for the imgainary bits: cos(2x)=cos2(x)-sin2(x) sin(2x)=2sin(x)cos(x) These identities are the correct ones.
CP
Answered by Cezar P. • Further Mathematics tutor
4967 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Sketch the curve y= ((3x+2)(x-3))/((x-2)(x+1)) and find values of y for which y>=3
A mass m=1kg, initially at rest and with x=10mm, is connected to a damper with stiffness k=24N/mm and damping constant c=0.2Ns/mm. Given that the differential equation of the system is given by d^2x/dt^2+(dx/dt *c/m)+kx/m=0, find the particular solution.
Does the following matrix A = (2 2 // 3 9) (upper row then lower row) have an inverse? If the matrix A^2 is applied as a transformation to a triangle T, by what factor will the area of the triangle change under the transformation?
A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0. Find dy/dx and d^2y/dx^2. Verify that C has a stationary point when x = 4