यदि `A = [{:( cos alpha ,,- sin alpha ) , ( sin alpha,, cos alpha):}] ` तथा A + A' = I, तो `alpha` का मान है

Options

A. ` (pi)/(6)`
B. `(pi)/(3)`
C. `pi`
D. `(3pi)/(2)`

Answer

B

Explanation

चुकि
`A = [{:( cos alpha ,,- sin alpha ) , ( sin alpha,, cos alpha):}] `

`A' = [{:( cos alpha ,, sin alpha ) , ( -sin alpha,, cos alpha):}] `

अब प्रश्न से

`[{:( cos alpha ,,- sin alpha ) , ( sin alpha,, cos alpha):}]` `+[{:( cos alpha ,, sin alpha ) , ( -sin alpha,, cos alpha):}] ``=[{:( 1 ,, 0 ) , ( 0,, 1):}] `

` [{:( cos alpha+cosalpha ,, -sin alpha+sin alpha ) , ( sin alpha+(-sin alpha),, cos alpha+cosalpha):}] ``=[{:( 1 ,, 0 ) , ( 0,, 1):}] `

`[{:( 2cos alpha ,,0 ) , ( 0,, 2cos alpha):}]` `=[{:( 1 ,, 0 ) , ( 0,, 1):}] `

`2cosalpha=1`

`cosalpha=1/2`

alpha=pi/3`