A=cosα-sinαsinαcosα and A32=0-110, then α may be
0
π32
π64
π16
Explanation for the correct option:
Step 1: Express the given data
We have been given that,
A=cosα-sinαsinαcosα&A32=0-110
We need to find the value of α.
We know, An=cosnα-sinnαsinnαcosnα
For, n=32,
⇒ A32=cos32α-sin32αsin32αcos32α
Step 2: Find the value of α
A32=cos32α-sin32αsin32αcos32α
⇒0-110=cos32α-sin32αsin32αcos32α
⇒cos32α=0
⇒ 32α=cos-10
⇒ 32α=π2
⇒ α=π32×2
⇒ α=π64
Therefore, option (C) is the correct answer.