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Properties Derived from Trigonometric Identities

The value of ...

Question

The value of $t a n^{2} (s e c^{- 1} 3) + c o t^{2} (c o s e c^{- 1} 4)$ is

A

20

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B

21

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C

23

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D

25

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Solution

The correct option is C 23
Let $S e c^{- 1} 3 = α, c o s e c^{- 1} 4 = β \Rightarrow t a n^{2} α + c o t^{2} β = 9 - 1 + 16 - 1 = 23$

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