Statement -1: `sin52^(@)+sin78^(@)+sin50^(@)=4cos26^(@)cos39^(@)cos25^(@)`
Statement-2: If `A+B+C=pi, then sinA+sin B+sinC=4cos""(A)/(2)cos""(B)/(2)cos""©/(2)`

Options

A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement -1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

A

Explanation

If `A+B+C=pi, then sinA+sinB+sinC`
`=2sin""(A+B)/(2)cos""(A-B)/(2)+2sin""(C)/(2)cos""(C)/(2)`
`=2cos""(C)/(2){cos""(A-B)/(2)+cos""(A+B)/(2)}=4cos""(A)/(2)cos""(B)/(2)cos""(C)/(2)`
So, statement-2 is true.
On replacing A by `52^(@),Bby78^(@)and C by 50^(@),` we obtain statement-1.
Hence, both the statements are true and statement-2 is a correct explanation for statement-1.