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If a^(2) + b^(2) = c^(2), c != 0, then f...

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

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.

Text Solution

Verified by Experts

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
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