e ,
P(k) : Ak =
cos
sin
sin
cos
k
k
k
k
θ
θ




−
θ
θ


Rationalised 2023-24
 MATHEMATICS
190
We want to prove that P(k + 1) is true whenever P(k) is true, i e ,
P(k + 1) : Ak+1 =
cos (
1)
sin (
1)
sin(
1)
cos (
1 )
k
k
k
k
+
θ
+
θ




−
+
θ
+
θ


Now
Ak+1 = Ak