Statement -1: If `a^(2)+b^(2)=c^(2),c ne 0` then the non zero solution of the equation `sin^(-1)((ax)/(c ))+sin^(-1)((bx)/(c))=sin^(-1)x` is `pm`1,. Statement-2: `sin^(-1)x+sin^(-1)y= sin^(-1)(x+y)`

Options

A. Statement-1 is 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.

Explanation

Clearly statement 2 is not true
we have
`c^(2)=a^(2)+b^(2)` so let `a=c cos alpha and b =c sin alpha` then
`sin^(-1)(ax)/(c )+sin^(-1)(bx)/(c )=sin^(-1)x`
`rarr sin^(-1)(x cos alpha) s+sin^(-1) (x sin alpha)=sin^(-1)x`
`rarr sin^(-1)(xcos alphasqrt(1=-x^(2))sin^(2)alpha)+x sin alpha sqrt(1-x^(2) cos^(2) alpha)`
`rarr cos alpha sqrt(1-x^(2)) alpha+sin alpha sqrt(1-x^(2) cos^(2) alpha=1)`
clearly `x=pm1` satisfies this equaiton