यदि `E (theta)=[(costheta" "sintheta),(-sin theta" " cos theta)]`, तो `E (alpha)E(beta)` किसके बराबर है

Options

A. `E(alpha beta)`
B. `E(alpha - beta)`
C. `E( alpha+ beta)`
D. `-E(alpha+beta)`

Answer

C

Explanation

`E(theta)=[(costheta" "sintheta),(-sintheta" "costheta)]`

`:. E(alpha)=[(cos alpha" "sinalpha),(-sinalpha" "cosalpha)]`

तथा `E(beta)=[(cosbeta" "sin beta),(-sinbeta" "cosbeta)]`

` :. E (alpha)*E(beta)`

`=[(cos alpha" "sinalpha),(-sin alpha" "cos alpha)][(cos beta" "sin beta),(-sin beta" "cos beta)]`

`[cos alphacos beta-sin alphasin beta``=cos(alpha+beta)]`
`[cos alphasin beta+sin alphacos beta``=sin(alpha+beta)]`

` =[(cos(alpha+beta)" "sin(alpha+beta)),(-sin(alpha+beta)" "cos(alpha+beta))]`

` = E(alpha+beta)`