Question

Number of solution of equation

sin^–1 x + n sin^–1(1 –x) = where n > 0, m £ 0 is-

• A. 3
• B. 1
• C. 2
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

sin^–1x is defined if –1 £ x £ 1 and sin^–1 (1 – x) is defined if

–1£ 1 – x £ 1 Ž 0 £ x £ 2

\ sin^–1 x + n sin^–1 (1 – x) is defined if 0 £ x £ 1 when

0 £ x £1, also 0 £ 1 – x £ 1

So 0 £ sin^–1 x £$\frac { \pi } { 2 }$

\ LHS ³ 0 & RHS £ 0, so equally holds if

LHS = RHS = 0

But LHS = 0 if sin^–1x and n sin^–1(1 – x) are simultaneously zero, which is impossible.