Correct option is B
We can use the subtraction formula for inverse sine: sin − 1 A − sin − 1 B = sin − 1 ( ( A 1 − B 2 − B 1 − A 2 ) ) Identify A and B A = 4 5 , B = 5 13 Compute 1 − A 2 and 1 − B 2 1 − A 2 = 1 − ( 4 5 ) 2 = 1 − 16 25 = 9 25 = 3 5 1 − B 2 = 1 − ( 5 13 ) 2 = 1 − 25 169 = 144 169 = 12 13 Apply the subtraction formula sin − 1 ( 4 5 ) − sin − 1 ( 5 13 ) = sin − 1 ( 4 5 ⋅ 12 13 − 5 13 ⋅ 3 5 ) = sin − 1 ( 48 65 − 15 65 ) = sin − 1 ( 33 65 ) \text{We can use the subtraction formula for inverse sine:} \\\sin^{-1} A - \sin^{-1} B = \sin^{-1} \left( \left( A \sqrt{1 - B^2} - B \sqrt{1 - A^2} \right) \right) \\\textbf{Identify A and B} \\A = \frac{4}{5}, \quad B = \frac{5}{13} \\\textbf{Compute } \sqrt{1 - A^2} \text{ and } \sqrt{1 - B^2} \\\sqrt{1 - A^2} = \sqrt{1 - \left( \frac{4}{5} \right)^2} = \sqrt{1 - \frac{16}{25}} = \sqrt{\frac{9}{25}} = \frac{3}{5} \\\sqrt{1 - B^2} = \sqrt{1 - \left( \frac{5}{13} \right)^2} = \sqrt{1 - \frac{25}{169}} = \sqrt{\frac{144}{169}} = \frac{12}{13} \\\textbf{Apply the subtraction formula} \\\sin^{-1} \left( \frac{4}{5} \right) - \sin^{-1} \left( \frac{5}{13} \right) = \sin^{-1} \left( \frac{4}{5} \cdot \frac{12}{13} - \frac{5}{13} \cdot \frac{3}{5} \right) \\= \sin^{-1} \left( \frac{48}{65} - \frac{15}{65} \right) = \sin^{-1} \left( \frac{33}{65} \right) We can use the subtraction formula for inverse sine: sin − 1 A − sin − 1 B = sin − 1 ( ( A 1 − B 2 − B 1 − A 2 ) ) Identify A and B A = 5 4 , B = 13 5 Compute 1 − A 2 and 1 − B 2 1 − A 2 = 1 − ( 5 4 ) 2 = 1 − 25 16 = 25 9 = 5 3 1 − B 2 = 1 − ( 13 5 ) 2 = 1 − 169 25 = 169 144 = 13 12 Apply the subtraction formula sin − 1 ( 5 4 ) − sin − 1 ( 13 5 ) = sin − 1 ( 5 4 ⋅ 13 12 − 13 5 ⋅ 5 3 ) = sin − 1 ( 65 48 − 65 15 ) = sin − 1 ( 65 33 )
English
80 Questions
160 Marks
60 Mins
, then which one of the following is true?
then which one of the following is correct?
is given by:
the principal value of
is:
