If ^ - 1 3 5 - ^ - 1 4 5 = ^ - 1 x, then x= - Vidyadip

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) ${\cos ^{ - 1}}\frac{3}{5} - {\sin ^{ - 1}}\frac{4}{5} = {\cos ^{ - 1}}x$

$ \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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