3 - 1 x = - 1 (4 x 3 - 3x), ;x

Put - 1 x = . ; ;Then, ;x = Now, 3 = )4 3 - 3 ) = (4 x 3 - 3x) 3 = - 1 (4 x 3 - 3x) 3 - 1 x = - 1 (4 x 3 - 3x) Hence, 3 - 1 x = - 1 (4 x 3 - 3x)

Inverse Trigonometric Functions — Class 12 Maths Solution

ncert exercise SA NCERT Ex. 2.2, Q. 2 , Page 47

Question

$3{\cos ^{ - 1}}x = {\cos ^{ - 1}}(4{x^3} - 3x),\;x \in \left[ {\frac{1}{2},\;1} \right]$

Step-by-step Solution

Put ${\cos ^{ - 1}}x = \theta .\;\;Then,\;x = \cos \theta$

Now, $\cos 3\theta = )4{\cos ^3}\theta - 3\cos \theta ) = (4{x^3} - 3x)$
$\Rightarrow$ $3\theta = {\cos ^{ - 1}}(4{x^3} - 3x)$
$\Rightarrow$ $3{\cos ^{ - 1}}x = {\cos ^{ - 1}}(4{x^3} - 3x)$

Hence, $3{\cos ^{ - 1}}x = {\cos ^{ - 1}}(4{x^3} - 3x)$

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