MCQ
If ${\cos ^{ - 1}}\frac{3}{5} - {\sin ^{ - 1}}\frac{4}{5} = {\cos ^{ - 1}}x,$ then $ x=$
- A$0$
- ✓$1$
- C$-1$
- D$2$
✓
Answer
Correct option: B.
$1$
b
(b) ${\cos ^{ - 1}}\frac{3}{5} - {\sin ^{ - 1}}\frac{4}{5} = {\cos ^{ - 1}}x$
(b) ${\cos ^{ - 1}}\frac{3}{5} - {\sin ^{ - 1}}\frac{4}{5} = {\cos ^{ - 1}}x$
$ \Rightarrow {\cos ^{ - 1}}\frac{3}{5} - {\cos ^{ - 1}}\sqrt {1 - \frac{{16}}{{25}}} = {\cos ^{ - 1}}x$
$ \Rightarrow {\cos ^{ - 1}}\frac{3}{5} - {\cos ^{ - 1}}\frac{3}{5} = {\cos ^{ - 1}}x$
$ \Rightarrow {\cos ^{ - 1}}x = 0 \Rightarrow x = 1$.
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