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Question
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
Options
–4
0
–1
4
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Solution
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to 0.
Explanation:
`"cosec" [sin^-1(-1/2)] - sec [cos^-1((-1)/2)]`
= `"cosec" [-sin^-1(1/2)] - sec [π - cos^-1((-1)/2)]`
= `"cosec" [- π/6] - sec [π - π/3]`
= `-"cosec" [π/6] - sec [(2π)/3]`
= – cosec 30° – sec 120°
= – cosec 30° – sec [(90° + 30°)]
= – 2 – [– cosec 30°]
= – 2 + cosec 30°
= – 2 + 2
= 0
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