The value of sinsin -11-3- -1 3-costan -11-2-tan -1 2

The correct option is A 1sin(sin^ 1 (1/3 )+sec^ 1(3) )+cos(tan^ 1 (1/2 )+tan^ 1(2) ) =sin(sin^ 1 (1/3 )+cos^ 1(1/3 ) )+cos(tan^ 1(1/2 ) )+cot^ 1(1/2 )=sinπ ...

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Byju's Answer

Standard XII

Mathematics

Composition of Inverse Trigonometric Functions and Trigonometric Functions

The value of ...

Question

The value of $s i n (s i n^{- 1} \frac{1}{3} + s e c^{- 1} 3) + c o s (t a n^{- 1} \frac{1}{2} + t a n^{- 1} 2)$ is

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Solution

The correct option is A
1

$s i n (s i n^{- 1} (\frac{1}{3}) + s e c^{- 1} (3)) + c o s (t a n^{- 1} (\frac{1}{2}) + t a n^{- 1} (2))$
$= s i n (s i n^{- 1} (\frac{1}{3}) + c o s^{- 1} (\frac{1}{3})) + c o s (t a n^{- 1} (\frac{1}{2})) + c o t^{- 1} (\frac{1}{2}) = s i n \frac{π}{2} + c o s$
$(∵ s i n^{- 1} x + c o s^{- 1} x = \frac{π}{2} a n d t a n^{- 1} x + c o s^{- 1} x = \frac{π}{2}) = 1$

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The correct option is A 1sin(sin−1(13)+sec−1(3))+cos(tan−1(12)+tan−1(2)) =sin(sin−1(13)+cos−1(13))+cos(tan−1(12))+cot−1(12)=sinπ2+cos (∵sin−1x+cos−1x=π2 and tan−1x+cos−1x=π2)=1

The value of $s i n (s i n^{- 1} \frac{1}{3} + s e c^{- 1} 3) + c o s (t a n^{- 1} \frac{1}{2} + t a n^{- 1} 2)$ is