The value of sin 2tan -1 1 3 -cos tan -1 2- 2 is equal to

The correct option is C 14 15 Simplifying , we get 2sin(tan^ 1(13))cos(tan^ 1(13))+cos^ 1(cos(13)) =2sin(sin^ 1(1√(10)))cos(cos^ 1(3√(10)))+13 ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

The value of ...

Question

The value of $sin (2 {tan}^{- 1} \frac{1}{3}) + cos ({tan}^{- 1} 2 \sqrt{2})$ is equal to

\frac{12}{13}

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\frac{13}{14}

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\frac{14}{15}

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None of these

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Solution

The correct option is C $\frac{14}{15}$
Simplifying , we get
$2 s i n (t a n^{- 1} (\frac{1}{3})) c o s (t a n^{- 1} (\frac{1}{3})) + c o s^{- 1} (c o s (\frac{1}{3}))$
$= 2 s i n (s i n^{- 1} (\frac{1}{\sqrt{10}})) c o s (c o s^{- 1} (\frac{3}{\sqrt{10}})) + \frac{1}{3}$
$= \frac{6}{10} + \frac{1}{3}$
$= \frac{3}{5} + \frac{1}{3}$
$= \frac{14}{15}$

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Q. The ages of students of 10^th class, in a school are as follows. The ages are given in years months.

14

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6, 13

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2, 16

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9, 14

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5, 14

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7, 14

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0,
15

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0, 15

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1, 16

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2, 14

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1, 13

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11, 16

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0, 14

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5, 14

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0,
14

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8, 14

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4, 15

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4, 15

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9, 15

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1, 14

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10, 14

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-

8

15

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1, 14

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1, 16

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10, 14

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0, 15

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0, 13

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6, 13

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11,
14

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3, 14

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8, 14

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7, 14

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8, 14

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1, 15

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0, 15

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1, 14

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4,
14

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9, 14

-

9, 14

-

10, 15

-

3, 14

-

9, 13

-

10, 13

-

2, 15

-

1,

Prepare a grouped frequency distribution table (classes; 13

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14, 14

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15, 15

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16, ....)

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The value of sin(2tan−113)+cos(tan−12√2) is equal to

The correct option is C 1415Simplifying , we get2sin(tan−1(13))cos(tan−1(13))+cos−1(cos(13))=2sin(sin−1(1√10))cos(cos−1(3√10))+13=610+13=35+13=1415

The value of $sin (2 {tan}^{- 1} \frac{1}{3}) + cos ({tan}^{- 1} 2 \sqrt{2})$ is equal to