Inverse Trigonometric Functions — Class 12 Maths Solution

exemplar fill FillBlank NCERT,Ex.2.3,Q.40,Page.40
Question

If $\cos \left( {{{\tan }^{ - 1}}x + {{\cot }^{ - 1}}\sqrt 3 } \right) = 0$, then the value of $x$ is

Step-by-step Solution

We have, $\cos \left( {{{\tan }^{ - 1}}x + {{\cot }^{ - 1}}\sqrt 3 } \right) = 0$

$\Rightarrow$ ${\tan ^{ - 1}}x + {\cot ^{ - 1}}\sqrt 3 = {\cos ^{ - 1}}0$

$\Rightarrow$ ${\tan ^{ - 1}}x + {\cot ^{ - 1}}\sqrt 3 = {\cos ^{ - 1}}\cos \frac{\pi }{2}$

$\Rightarrow$ ${\tan ^{ - 1}}x + {\cot ^{ - 1}}\sqrt 3 = \frac{\pi }{2}$

$\Rightarrow$ ${\tan ^{ - 1}}x = \frac{\pi }{2} - {\cot ^{ - 1}}\sqrt 3$
$\Rightarrow$ ${\tan ^{ - 1}}x = {\tan ^{ - 1}}\sqrt 3$

$therefore,$ $x = \sqrt 3$

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