1
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

If the inverse trigonometric functions take principal values then

$${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right) + {2 \over 5}\sin \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right)} \right)$$ is equal to :

A
0
B
$${\pi \over 4}$$
C
$${\pi \over 3}$$
D
$${\pi \over 6}$$
2
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

The value of $${\tan ^{ - 1}}\left( {{{\cos \left( {{{15\pi } \over 4}} \right) - 1} \over {\sin \left( {{\pi \over 4}} \right)}}} \right)$$ is equal to :

A
$$- {\pi \over 4}$$
B
$$- {\pi \over 8}$$
C
$$- {{5\pi } \over {12}}$$
D
$$- {{4\pi } \over 9}$$
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Let $$x * y = {x^2} + {y^3}$$ and $$(x * 1) * 1 = x * (1 * 1)$$.

Then a value of $$2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2} - 2} \over {{x^4} + {x^2} + 2}}} \right)$$ is :

A
$${\pi \over 4}$$
B
$${\pi \over 3}$$
C
$${\pi \over 2}$$
D
$${\pi \over 6}$$
4
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

The set of all values of k for which

$${({\tan ^{ - 1}}x)^3} + {({\cot ^{ - 1}}x)^3} = k{\pi ^3},\,x \in R$$, is the interval :

A
$$\left[ {{1 \over {32}},{7 \over 8}} \right)$$
B
$$\left( {{1 \over {24}},{{13} \over {16}}} \right)$$
C
$$\left[ {{1 \over {48}},{{13} \over {16}}} \right]$$
D
$$\left[ {{1 \over {32}},{9 \over 8}} \right)$$
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