Cos-cos-1-1-7- - sin-1-1-7- -

Explanation for the correct option:Let X=cos[cos^ 1( 1/7)+sin^ 1( 1/7)]We know that, 𝑐𝑜𝑠^ 1𝑥+𝑠𝑖𝑛^ 1𝑥=π/2∴cos^ 1( 1/7)+sin^ 1( 1/7)=π/2⇒X=cos(π ...

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Standard XII

Mathematics

Parametric Differentiation

cos[cos^-1(-1...

Question

$\cos [\cos^{- 1} (- \frac{1}{7}) + \sin^{- 1} (- \frac{1}{7})] = ?$

$- \frac{1}{3}$

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$0$

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$\frac{1}{3}$

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$\frac{4}{9}$

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Solution

The correct option is B
$0$

Explanation for the correct option:
Let $X = \cos [\cos^{- 1} (- \frac{1}{7}) + \sin^{- 1} (- \frac{1}{7})]$
We know that,
$c o s^{- 1} x + s i n^{- 1} x = \frac{π}{2}$
$∴ \cos^{- 1} (- \frac{1}{7}) + \sin^{- 1} (- \frac{1}{7}) = \frac{π}{2}$
$\Rightarrow$ $X = \cos (\frac{π}{2})$
$= 0$
Hence, Option ‘B’ is Correct.

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coscos-1-17+sin-1-17=?

The correct option is B 0Explanation for the correct option:Let X=coscos−1−17+sin−1−17We know that, cos−1x+sin−1x=π2∴cos−1−17+sin−1−17=π2⇒X=cosπ2 =0Hence, Option ‘B’ is Correct.

$\cos [\cos^{- 1} (- \frac{1}{7}) + \sin^{- 1} (- \frac{1}{7})] = ?$