The least value of cosec 2x + 25 sec 2x is

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Solution

Q.
The least value of $\cos e c^{2} x + 25 s e c^{2} x$ is

1 0

2 26

3 28

4 36

Ans.
(4)

$c o s e c^{2} x + 25 \sec^{2} x$

$= 1 + \cot^{2} x + 25 (1 + \tan^{2} x)$

$= 26 + \cot^{2} x + 25 \tan^{2} x$

$= 26 + 10 + {(\cot x - 5 \tan x)}^{2} \geq 36$

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