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Question
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
Options
`1/5`
`2/5`
0
1
Solution
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to `2/5`.
Explanation:
We have, `cos(sin^-1 2/5 + cos^-1x)` = 0
⇒ `sin^-1 2/5 + cos^-1x = cos^-1 0`
⇒ `sin^-1 2/5 + cos^-1x = pi/2`
⇒ `cos^-1x = pi/2 - sin^-1 2/5`
⇒ `cos^-1x = cos^-1 2/5` .....`(because cos^-1x +sin^-1x = pi/2)`
∴ x = `2/5`
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