The value of s i n − 1 { c o t ( s i n − 1 √ ( 2 − √ 3 4 ) + c o s − 1 √ 12 4 + s e c − 1 √ 2 ) } is: Options: A . &nbsp 0 B . &nbsp π 4 C . &nbsp π 6 D . &nbsp π 2

Answer: Option A : A c o s − 1 √ 12 4 = c o s − 1 √ 3 2 = π 6 , s e c − 1 √ 2 = π 4 s i n − 1 √ 2 − √ 3 4 = s i n − 1 √ 4 − 2 √ 3 8 = s i n − 1 √ 3 − 1 2 √ 2 = π 12 ∴ s i n − 1 √ 2 − √ 3 4 + c o s − 1 √ 12 4 + s e c − 1 √ 2 = π 2 and s i n − 1 ( c o t π 2 ) = s i n − 1 0 = 0

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Discussion Forum : Inverse Trigonometric Functions

Question -

The value of $s i n^{- 1} {c o t (s i n^{- 1} \sqrt{(\frac{2 - \sqrt{3}}{4})} + c o s^{- 1} \frac{\sqrt{12}}{4} + s e c^{- 1} \sqrt{2})}$ is:

Options:

A .

0

B .

\frac{π}{4}

C .

\frac{π}{6}

D .

\frac{π}{2}

Answer: Option A
:
A

c o s^{- 1} \frac{\sqrt{12}}{4} = c o s^{- 1} \frac{\sqrt{3}}{2} = \frac{π}{6}, s e c^{- 1} \sqrt{2} = \frac{π}{4}

s i n^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}} = s i n^{- 1} \sqrt{\frac{4 - 2 \sqrt{3}}{8}} = s i n^{- 1} \frac{\sqrt{3} - 1}{2 \sqrt{2}} = \frac{π}{12}

∴

s i n^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}} + c o s^{- 1} \frac{\sqrt{12}}{4} + s e c^{- 1} \sqrt{2} = \frac{π}{2}

and

s i n^{- 1} (c o t \frac{π}{2}) = s i n^{- 1} 0 = 0

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Discussion Forum : Inverse Trigonometric Functions

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