If ( - 1 5 + - 1 x ) = 0 , then x is equal to

We have, ( - 1 5 + - 1 x ) = 0 5 + - 1 x = - 1 0 5 + - 1 x = - 1 2 5 + - 1 x = 2 x = 2 - - 1 5 x = - 1 5 therefore, x = 5

Inverse Trigonometric Functions — Class 12 Maths Solution

exemplar objective MCQ NCERT,Ex.2.3,Q.26,Page.38

Question

If $\cos \left( {{{\sin }^{ - 1}}\frac{2}{5} + {{\cos }^{ - 1}}x} \right) = 0$, then $x$ is equal to

(a) $\frac{1}{5}$
(b) $\frac{2}{5}$ ✓ Correct
(c) 0
(d) 1

Step-by-step Solution

We have, $\cos \left( {{{\sin }^{ - 1}}\frac{2}{5} + {{\cos }^{ - 1}}x} \right) = 0$
$\Rightarrow$ ${\sin ^{ - 1}}\frac{2}{5} + {\cos ^{ - 1}}x = {\cos ^{ - 1}}0$

$\Rightarrow$ ${\sin ^{ - 1}}\frac{2}{5} + {\cos ^{ - 1}}x = {\cos ^{ - 1}}\cos \frac{\pi }{2}$

$\Rightarrow$ ${\sin ^{ - 1}}\frac{2}{5} + {\cos ^{ - 1}}x = \frac{\pi }{2}$

$\Rightarrow$ ${\cos ^{ - 1}}x = \frac{\pi }{2} - {\sin ^{ - 1}}\frac{2}{5}$

$\Rightarrow$ ${\cos ^{ - 1}}x = {\cos ^{ - 1}}\frac{2}{5}$
$therefore,$ $x = \frac{2}{5}$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Inverse Trigonometric Functions. Curated by Sachin Sharma. Free for all students.