Q62 / 160 · AP EAMCET 2022 (05 Jul Shift 2) · Mathematics

$\sec ^2 x+5 \tan x+5=$

  • Correct answer
    A
    $(\tan x+2)(\tan x+3)$
  • B
    $(\tan \mathrm{x}+1)(\tan \mathrm{x}+5)$
  • C
    $(\tan x-2)(\tan x-3)$
  • D
    $(\sin x+2)(\sin x+5)$

Solution

$1+\tan ^2 x+5 \tan x+5$ $\begin{aligned} & =\tan ^2 x+5 \tan x+6 \\ & =\tan ^2 x+2 \tan x+3 \tan x+6 \\ & =\tan x(\tan x+2)+3(\tan x+2) \\ & =(\tan x+2)(\tan x+3)\end{aligned}$

Hence, the correct answer is option: 'A'.

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