Evaluate Each Expression:

Question

a) 2cos^2 2π/3 - 1

b) cos^2 7π/8 - sin^2 7π/8

c)2sin 11π/12 x cos 11π/12

d) 1 - 2sin^2 π/2

Answer 1

a)2cos^2 2π/3 - 1
= cos 4π/3 , from cos 2A = 2cos^2 A - 1 identity
= - cos π/3
= - 1/2, from the 30-60-90° right-angled triangle

b) cos^2 7π/8 - sin^2 7π/8
= cos 7π/4 , from cos 2A = cos^2 A - sin^2 A
= cos π/4
= √2/2 , from the 45-45-90° right-angled triangle

c) 2sin 11π/12 x cos 11π/12
= sin 11π/6 , from sin 2A = 2sinAcosA
= - sin π/6
= -1/2

d) 1 - 2sin^2 π/2
your turn, hint: cos 2A = ..... , there are 3 versions, we have used 2 of them