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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

The minimum v...

Question

The minimum value of $t a n^{2} α + c o t^{2} α$ is

A

2

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B

3

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C

1

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D

0

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Solution

The correct option is A 2
$(t a n α - c o t α)^{2} = t a n^{2} α + c o t^{2} α - 2 t a n α . c o t α$
Now
Since $t a n α . c o t α = 1$ and for minimum value of $t a n^{2} α + c o t^{2} α$ , we would get some $α$ for which $t a n α - c o t α = 0$
$∴$ minimum value of $t a n^{2} α + c o t^{2} α = 2$

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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

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