The value of sin-tan -1-3-cos -1-3-2-

The correct option is A 1sin[tan^ 1( √(3))+cos^ 1( √(3)/2 ) ] =sin[ tan^ 1√(3)+π cos^ 1√(3)/2 ] [∵ tan^ 1( x)= tan^ 1x and cos^ 1( x)=π cos^ 1x ] =sin[ π/3+π ...

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Byju's Answer

Standard XII

Mathematics

Properties Derived from Trigonometric Identities

The value of ...

Question

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

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Solution

The correct option is A
1

$s i n [t a n^{- 1} (- \sqrt{3}) + c o s^{- 1} (- \frac{\sqrt{3}}{2})]$
$= s i n [- t a n^{- 1} \sqrt{3} + π - c o s^{- 1} \frac{\sqrt{3}}{2}]$
$[∵ t a n^{- 1} (- x) = - t a n^{- 1} x a n d c o s^{- 1} (- x) = π - c o s^{- 1} x]$
$= s i n [- \frac{π}{3} + π - \frac{π}{6}] = s i n \frac{π}{2}$

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