If x - 1 or x -1- then cosec-1 x -A- 1-sin -1xB- -1-2-xC- sin -11-xD- None of these

The correct option is C sin^ 1 ( 1/x )Let cosec^ 1(x) = y Since, x ⩾ 1 or x ⩽ 1; we can write x = cosec(y) x = 1/sin(y) Or sin(y) = 1/x y = sin^ 1 ( 1/ ...

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Standard XI

Mathematics

Trigonometric Ratios of Multiples of an Angle

If x ⩾ 1 or x...

Question

$I f x ⩾ 1 o r x ⩽ - 1, t h e n c o s e c^{- 1} (x) =$

s e c^{- 1} (\frac{π}{2} - x)

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s i n^{- 1} (\frac{1}{x})

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\frac{1}{s i n^{- 1} (x)}

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None of these

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Solution

The correct option is B $s i n^{- 1} (\frac{1}{x})$
$L e t c o s e c^{- 1} (x) = y S i n c e, x ⩾ 1 o r x ⩽ - 1; w e c a n w r i t e - x = c o s e c (y) x = \frac{1}{s i n (y)} O r s i n (y) = \frac{1}{x} y = s i n^{- 1} (\frac{1}{x})$

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If x⩾1 or x ⩽−1, then cosec−1(x)=

The correct option is B sin−1(1x)Let cosec−1(x)=ySince,x⩾1orx⩽−1; we can write−x=cosec(y)x=1sin(y)Or sin(y)=1xy=sin−1(1x)

$I f x ⩾ 1 o r x ⩽ - 1, t h e n c o s e c^{- 1} (x) =$

The correct option is B $s i n^{- 1} (\frac{1}{x})$
$L e t c o s e c^{- 1} (x) = y S i n c e, x ⩾ 1 o r x ⩽ - 1; w e c a n w r i t e - x = c o s e c (y) x = \frac{1}{s i n (y)} O r s i n (y) = \frac{1}{x} y = s i n^{- 1} (\frac{1}{x})$