यदि `sin(A+B)=sinA" "cosB+cosA" "sinB` है तो `sin75^@` का मान ज्ञात करे ?

Options

A. `(sqrt(3)+1)/(sqrt(2))`
B. `(sqrt(2)+1)/(2sqrt(2))`
C. `(sqrt(3)+1)/(2sqrt(2))`
D. `(sqrt(3)+1)/(2)`

Answer

c

Explanation

`Sin(A+B)=sinA cosB+cosA.sinB`.
Shortcut method
Put `A=45^(@)`
`B=30^(@)`
`B=30^(@)`
`sin45^(@)+30^(@)=sin45^(@)cos30^(@)+cos45^(@).sin30^(@)`
`sin75^(@)=(1)/sqrt(2)xxsqrt(3)/(2)+(1)/sqrt(2)xx(1)/(2)`
`rArrsqrt(3)/(2sqrt(2))+(1)/(2sqrt(2))`
`rArr(sqrt(2)+1)/(2sqrt(2))`