AP EAMCET · Maths · Trigonometric Equations
\(\sec ^2 x+5 \tan x+5=\)
- A \((\tan x+2)(\tan x+3)\)
- B \((\tan \mathrm{x}+1)(\tan \mathrm{x}+5)\)
- C \((\tan x-2)(\tan x-3)\)
- D \((\sin x+2)(\sin x+5)\)
Answer & Solution
Correct Answer
(A) \((\tan x+2)(\tan x+3)\)
Step-by-step Solution
Detailed explanation
\(1+\tan ^2 x+5 \tan x+5\) \(\begin{aligned} & =\tan ^2 x+5 \tan x+6 \\ & =\tan ^2 x+2 \tan x+3 \tan x+6 \\ & =\tan x(\tan x+2)+3(\tan x+2) \\ & =(\tan x+2)(\tan x+3)\end{aligned}\)
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