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Trigonometric Ratios of Compound Angles

If sinsin -11...

Question

If $s i n (s i n^{- 1} \frac{1}{5} + c o s^{- 1} x) = 1$ , then x is equal to

A

1

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B

0

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C

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D

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Solution

The correct option is D
$s i n^{- 1} \frac{1}{5} + c o s^{- 1} x = \frac{π}{2}$
$∴ s i n^{- 1} \frac{1}{5} = \frac{π}{2} - c o s^{- 1} x = s i n^{- 1} x$
$∴ x = \frac{1}{5} .$

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t a n^{- 1} (\frac{1}{4}) + t a n^{- 1} = (\frac{2}{9}) = \frac{1}{2} c o s^{- 1} x,

then x is equal to

sin ({sin}^{- 1} \frac{1}{5} + {cos}^{- 1} x) = 1

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\begin{matrix} sin ({sin}^{- 1} \frac{1}{5} + {cos}^{- 1} x) = 1 \end{matrix}

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sin ({sin}^{- 1} \frac{1}{5} + {cos}^{- 1} x) = 1

, then find the value of

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sin ({sin}^{- 1} \frac{1}{5} + {cos}^{- 1} x) = 1

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