What is `sin^(2)66(1^(@))/(2)-sin^(2)23(1^(@))/(2)` equal to ?

Options

A. `sin47^(@)`
B. `cos47^(@)`
C. `2sin47^(@)`
D. `2cos47^(@)`

Answer

B

Explanation

`sin^(2)66(1^(@))/(2)-sin^(2)23(1^(@))/(2)`
`=[sin(90^(@)-23(1^(@))/(2))]^(2)-sin^(2)23(1^(@))/(2)`
`=cos^(2)23(1^(@))/(2)-sin^(2)23(1^(@))/(2)`
`=cos2(23(1^(@))/(2))=cos47^(@)`
`(becausecos2A=cos^(2)A-sin^(2)A)`
`=cos[2xx((47)/(2))]=cos47^(@)`