JEE Main 2020 (Online) 5th September Morning Slot | Inverse Trigonometric Functions Question 39 | Mathematics

JEE Main 2020 (Online) 5th September Morning Slot

MCQ (Single Correct Answer)

-1

If S is the sum of the first 10 terms of the series

$${\tan ^{ - 1}}\left( {{1 \over 3}} \right) + {\tan ^{ - 1}}\left( {{1 \over 7}} \right) + {\tan ^{ - 1}}\left( {{1 \over {13}}} \right) + {\tan ^{ - 1}}\left( {{1 \over {21}}} \right) + ....$$

then tan(S) is equal to :

$${10 \over {11}}$$

$${5 \over {11}}$$

-$${6 \over {5}}$$

$${5 \over {6}}$$

JEE Main 2020 (Online) 3rd September Morning Slot

MCQ (Single Correct Answer)

-1

2$$\pi $$ - $$\left( {{{\sin }^{ - 1}}{4 \over 5} + {{\sin }^{ - 1}}{5 \over {13}} + {{\sin }^{ - 1}}{{16} \over {65}}} \right)$$ is equal to :

$${{7\pi } \over 4}$$

$${{5\pi } \over 4}$$

$${{3\pi } \over 2}$$

$${\pi \over 2}$$

JEE Main 2019 (Online) 12th April Morning Slot

MCQ (Single Correct Answer)

-1

The value of $${\sin ^{ - 1}}\left( {{{12} \over {13}}} \right) - {\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ is equal to :

$$\pi - {\sin ^{ - 1}}\left( {{{63} \over {65}}} \right)$$

$${\pi \over 2} - {\sin ^{ - 1}}\left( {{{56} \over {65}}} \right)$$

$${\pi \over 2} - {\cos ^{ - 1}}\left( {{9 \over {65}}} \right)$$

$$\pi - {\cos ^{ - 1}}\left( {{{33} \over {65}}} \right)$$

JEE Main 2019 (Online) 10th April Evening Slot

MCQ (Single Correct Answer)

-1

If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha $$,where –1 $$ \le $$ x $$ \le $$ 1, – 2 $$ \le $$ y $$ \le $$ 2, x $$ \le $$ $${y \over 2}$$ , then for all x, y, 4x² – 4xy cos $$\alpha $$ + y² is equal to :

4 sin² $$\alpha $$

2 sin² $$\alpha $$

4 sin² $$\alpha $$ - 2x²y²

4 cos² $$\alpha $$ + 2x²y²

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