Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4 sin3θ

2. Find exact value of (a) sin-(-1) (b) cos-11 (c) tan-1 /3 (d) sin(sin¬' 0.8) (e) tan-'(tan ) (f) sin-(sin 2) (hint: 2 radians, not 2 degree)

Show that sec(z) – cos(z) + csc(z) – sin(z) – sin(z) tan(z) = cos(z) cot(z)

If A = A-¹ = 4e5t sin (7t) 6e5t cos(7t) 18 -4e²t cos(7t) 6e²t sin(7t) I " then

Verify that 2tan (x/2)= (sin2x+1-cos2)/(sin x(1+cos x)

Let F = (cos(5t), sin(3t) , 5t“) and G = (t cos(5t), cos(5t), Find F +G = (5t^4)+sin(3t)+t^4(cos(5t))+5e^4t